Question

Two supplementary angles are such that one is 4/5 of the other. Find the measure of both the angles​

Answer 1

Step-by-step explanation:

1st angle = x

2nd angle = 4x/5

Sum is 180° as they both are supplementary angles.

x + 4x/5 = 180°

5x/5 + 4x/5 = 180°

9x/5 = 180°

x = 180° × 5/9

x = 100°

1st angle = 100°

2nd angle = 4/5 × 100°

= 80°

Answer 2

${\large{\bold{\rm{\underline{Understanding \; the \; question}}}}}$

★ This question says that two supplementary angles are such that the measure of one angle is 4/5 of the measure of the other angle. We have to find out the measure of both the angles.

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ Two supplementary angles are such that the measure of one angle is 4/5 of the measure of the other angle.

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ The measure of the angle 1st.

★ The measure of the angle 2nd.

${\large{\bold{\rm{\underline{Solution}}}}}$

★ The measure of the angle 1st = 100°

★ The measure of the angle 2nd = 80°

${\large{\bold{\rm{\underline{Knowledge \; required}}}}}$

★ Supplementary angles - Supplementary angles are those angles whose sum is always equal to 180°

${\large{\bold{\rm{\underline{Assumptions}}}}}$

★ Let the angle 1st be a

★ Let the angle 2nd be b

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

_______________________

~ As in the question it is given that the supplementary angles are such that the measure of one angle is 4/5 of the measure of the other angle. Henceforth,

${\rm{:\implies a = 4/5 \: times \: of \: b}}$

${\rm{:\implies a = 4/5 \times b}}$

${\rm{:\implies a = 4b/5}}$ Eq. (1)

_______________________

~ Now as we already discussed that the sum of supplementry angles is always 180°. Henceforth,

${\rm{:\implies a \: + \: b \: = 180 \degree}}$

${\rm{:\implies 4b/5 \: + b \: = 180 \degree}}$

${\rm{:\implies 4b \: + 5b/5 \: = 180 \degree}}$

${\rm{:\implies 9b/5 \: = 180 \degree}}$

${\rm{:\implies 9b \: = 180 \times 5}}$

${\rm{:\implies 9b \: = 900}}$

${\rm{:\implies b \: = 900/9}}$

${\rm{:\implies b \: = 100 \degree}}$

${\underline{\frak{b \: measure \: 100 \degree}}}$

_______________________

~ Now let's imply the value of b as 100 in the eq (1)..!

${\rm{:\implies a \: = 4b/5}}$

${\rm{:\implies a \: = 4(100)/5}}$

${\rm{:\implies a \: = 400/5}}$

${\rm{:\implies a \: = 80 \degree}}$

${\underline{\frak{a \: measure \: 80 \degree}}}$

_______________________

Answer 3

${\large{\bold{\rm{\underline{Understanding \; the \; question}}}}}$

★ This question says that two supplementary angles are such that the measure of one angle is 4/5 of the measure of the other angle. We have to find out the measure of both the angles.

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ Two supplementary angles are such that the measure of one angle is 4/5 of the measure of the other angle.

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ The measure of the angle 1st.

★ The measure of the angle 2nd.

${\large{\bold{\rm{\underline{Solution}}}}}$

★ The measure of the angle 1st = 100°

★ The measure of the angle 2nd = 80°

${\large{\bold{\rm{\underline{Knowledge \; required}}}}}$

★ Supplementary angles - Supplementary angles are those angles whose sum is always equal to 180°

${\large{\bold{\rm{\underline{Assumptions}}}}}$

★ Let the angle 1st be a

★ Let the angle 2nd be b

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

_______________________

~ As in the question it is given that the supplementary angles are such that the measure of one angle is 4/5 of the measure of the other angle. Henceforth,

${\rm{:\implies a = 4/5 \: times \: of \: b}}$

${\rm{:\implies a = 4/5 \times b}}$

${\rm{:\implies a = 4b/5}}$ Eq. (1)

_______________________

~ Now as we already discussed that the sum of supplementry angles is always 180°. Henceforth,

${\rm{:\implies a \: + \: b \: = 180 \degree}}$

${\rm{:\implies 4b/5 \: + b \: = 180 \degree}}$

${\rm{:\implies 4b \: + 5b/5 \: = 180 \degree}}$

${\rm{:\implies 9b/5 \: = 180 \degree}}$

${\rm{:\implies 9b \: = 180 \times 5}}$

${\rm{:\implies 9b \: = 900}}$

${\rm{:\implies b \: = 900/9}}$

${\rm{:\implies b \: = 100 \degree}}$

${\underline{\frak{b \: measure \: 100 \degree}}}$

_______________________

~ Now let's imply the value of b as 100 in the eq (1)..!

${\rm{:\implies a \: = 4b/5}}$

${\rm{:\implies a \: = 4(100)/5}}$

${\rm{:\implies a \: = 400/5}}$

${\rm{:\implies a \: = 80 \degree}}$

${\underline{\frak{a \: measure \: 80 \degree}}}$

_______________________

Answer 4

${\large{\bold{\rm{\underline{Understanding \; the \; question}}}}}$

★ This question says that two supplementary angles are such that the measure of one angle is 4/5 of the measure of the other angle. We have to find out the measure of both the angles.

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ Two supplementary angles are such that the measure of one angle is 4/5 of the measure of the other angle.

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ The measure of the angle 1st.

★ The measure of the angle 2nd.

${\large{\bold{\rm{\underline{Solution}}}}}$

★ The measure of the angle 1st = 100°

★ The measure of the angle 2nd = 80°

${\large{\bold{\rm{\underline{Knowledge \; required}}}}}$

★ Supplementary angles - Supplementary angles are those angles whose sum is always equal to 180°

${\large{\bold{\rm{\underline{Assumptions}}}}}$

★ Let the angle 1st be a

★ Let the angle 2nd be b

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

_______________________

~ As in the question it is given that the supplementary angles are such that the measure of one angle is 4/5 of the measure of the other angle. Henceforth,

${\rm{:\implies a = 4/5 \: times \: of \: b}}$

${\rm{:\implies a = 4/5 \times b}}$

${\rm{:\implies a = 4b/5}}$ Eq. (1)

_______________________

~ Now as we already discussed that the sum of supplementry angles is always 180°. Henceforth,

${\rm{:\implies a \: + \: b \: = 180 \degree}}$

${\rm{:\implies 4b/5 \: + b \: = 180 \degree}}$

${\rm{:\implies 4b \: + 5b/5 \: = 180 \degree}}$

${\rm{:\implies 9b/5 \: = 180 \degree}}$

${\rm{:\implies 9b \: = 180 \times 5}}$

${\rm{:\implies 9b \: = 900}}$

${\rm{:\implies b \: = 900/9}}$

${\rm{:\implies b \: = 100 \degree}}$

${\underline{\frak{b \: measure \: 100 \degree}}}$

_______________________

~ Now let's imply the value of b as 100 in the eq (1)..!

${\rm{:\implies a \: = 4b/5}}$

${\rm{:\implies a \: = 4(100)/5}}$

${\rm{:\implies a \: = 400/5}}$

${\rm{:\implies a \: = 80 \degree}}$

${\underline{\frak{a \: measure \: 80 \degree}}}$

_______________________

Answer 5

${\large{\bold{\rm{\underline{Understanding \; the \; question}}}}}$

★ This question says that two supplementary angles are such that the measure of one angle is 4/5 of the measure of the other angle. We have to find out the measure of both the angles.

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ Two supplementary angles are such that the measure of one angle is 4/5 of the measure of the other angle.

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ The measure of the angle 1st.

★ The measure of the angle 2nd.

${\large{\bold{\rm{\underline{Solution}}}}}$

★ The measure of the angle 1st = 100°

★ The measure of the angle 2nd = 80°

${\large{\bold{\rm{\underline{Knowledge \; required}}}}}$

★ Supplementary angles - Supplementary angles are those angles whose sum is always equal to 180°

${\large{\bold{\rm{\underline{Assumptions}}}}}$

★ Let the angle 1st be a

★ Let the angle 2nd be b

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

_______________________

~ As in the question it is given that the supplementary angles are such that the measure of one angle is 4/5 of the measure of the other angle. Henceforth,

${\rm{:\implies a = 4/5 \: times \: of \: b}}$

${\rm{:\implies a = 4/5 \times b}}$

${\rm{:\implies a = 4b/5}}$ Eq. (1)

_______________________

~ Now as we already discussed that the sum of supplementry angles is always 180°. Henceforth,

${\rm{:\implies a \: + \: b \: = 180 \degree}}$

${\rm{:\implies 4b/5 \: + b \: = 180 \degree}}$

${\rm{:\implies 4b \: + 5b/5 \: = 180 \degree}}$

${\rm{:\implies 9b/5 \: = 180 \degree}}$

${\rm{:\implies 9b \: = 180 \times 5}}$

${\rm{:\implies 9b \: = 900}}$

${\rm{:\implies b \: = 900/9}}$

${\rm{:\implies b \: = 100 \degree}}$

${\underline{\frak{b \: measure \: 100 \degree}}}$

_______________________

~ Now let's imply the value of b as 100 in the eq (1)..!

${\rm{:\implies a \: = 4b/5}}$

${\rm{:\implies a \: = 4(100)/5}}$

${\rm{:\implies a \: = 400/5}}$

${\rm{:\implies a \: = 80 \degree}}$

${\underline{\frak{a \: measure \: 80 \degree}}}$

_______________________