Question

Two supplementary angles are such that the measure of one angle is 4/5 of the measure of the other anglw .Find the measure of the angles
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Answer 1

✬ 1st Angle = 100° ✬

✬ 2nd Angle = 80° ✬

Step-by-step explanation:

Given:

• There are two supplementary angles.
• Measure of one angle is 4/5 times of another one.

To Find:

• What is the measure of both angles ?

Solution: Let the two angles be x and y. Where

➟ x = 4/5 times of y

➟ x = 4/5 × y

➟ x = 4y/5ㅤㅤㅤㅤㅤeqⁿ i

As we know that ,

★ Sum of Supplementary angles = 180° ★

$\implies{\rm }$ x + y = 180°

$\implies{\rm }$ 4y/5 + y = 180°

$\implies{\rm }$ 4y + 5y/5 = 180°

$\implies{\rm }$ 9y = 180° × 5

$\implies{\rm }$ 9y = 900°

$\implies{\rm }$ y = 900°/9

$\implies{\rm }$ y = 100°

So the measure of one angle is 100° and of other is -

➫ x = 4/5 × 100

➫ x = 4 × 20

➫ x = 80°

Hence, two angles are of 100° and 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)..!

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

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

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

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

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

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