Question

If the measures of
complementary pair of
angles are in a ratio 1:5,
then what is the measure
of the smaller angle?
1 15°
2 18°
3 30°
4 10°
​

Answer 1

Answer:

• Option (1) correct. Measure of smaller angle is 15°.

Step-by-step explanation:

Given :-

• Ratio of complementary pair of angles is 1:5.

To find :-

• Measure of smaller angle.

Solution :-

We know,

Sum of two complementary angles is 90°.

Let, First complementary angle 1x or x.

And, Second complementary angle be 5x.

So,

$\rightarrow$ x + 5x = 90°

$\rightarrow$ 6x = 90°

$\rightarrow$ x = 90°/6

$\rightarrow$ x = 15°.

Verification :-

$\rightarrow$ x + 5x = 90°

• Put x = 15°

$\rightarrow$ 15° + 5× 15° =90°

$\rightarrow$ 15° + 75° = 90°

$\rightarrow$ 90° = 90°

$\boxed{\sf Hence \: Verified}$

Angles :-

First angle = x = 15°

So, First angle is 15°.

Second angle = 5x = 5×15° = 75°

Thus, Second angle is 75°

Here, First angle is smaller.

Therefore,

Smaller angle is 15°.

1) Option is correct.

Answer 2

Correct Question-:

• If the measures of complementary pair of angles are in a ratio 1:5 . Then what is the measure of the smaller angle ?

AnswEr-:

• $\underline{\boxed{\star{\sf{\purple{The \: measure\:of\:smaller\:angle\:is\:15⁰,and\:The\:option\:1\:is\:correct. }}}}}$

Explanation-:

Given -:

• The measures of complementary pair of angles are in a ratio 1:5 .

To Find -:

• What is the measure of the smaller angle ?

Solution -:

We know that ,

• $\underline{\boxed{\star{\sf{\purple{The\:Sum\:of\:Complementary \:angle\:is\:90⁰}}}}}$

• Let the complementary pair of angle be 1x or x and 5x .

Now ,

• $\implies {\large{\sf{ Complementary _{Angles}=x + 5x = 90⁰}}}$
• $\implies {\large{\sf{ Complementary _{Angles}=6x = 90⁰}}}$
• $\implies {\large{\sf{ Complementary _{Angles}= x =\frac{ 90}{6}}}}$
• $\implies {\large{\sf{ Complementary _{Angles}=x = 15⁰}}}$

Therefore,

• $\underline{\boxed{\star{\sf{\purple{x =15⁰ }}}}}$

Now ,

Then pairs of complementary angles are -:

• 1st Angle = x = 15⁰
• 2nd Angle = 5x = 5 × 15 = 75⁰

Hence ,

• $\underline{\boxed{\star{\sf{\purple{The\:pair\:of\:two\:complementary \:Angles \:are\:15⁰\:and\:75⁰\:}}}}}$ -----[1]
• $\underline{\boxed{\star{\sf{\purple{The \: measure\:of\:smaller\:angle\:is\:15⁰,and\:The\:option\:1\:is\:correct. }}}}}$

_________________________________

♤ Verification ♤

• $\underline{\boxed{\star{\sf{\purple{The\:Sum\:of\:Complementary \:angle\:is\:90⁰}}}}}$

Here,

• 1st Angle = 15⁰
• 2nd Angle = 75⁰________ [From 1]

Now ,

• $\implies {\large{\sf{ Complementary _{Angles}=15⁰ + 75⁰ = 90⁰}}}$
• $\implies {\large{\sf{ Complementary _{Angles}=90⁰ = 90⁰}}}$

Therefore,

• $\underline{\boxed{\star{\sf{\purple{LHS\: =\: RHS }}}}}$

• $\underline{\boxed{\star{\sf{\green{Hence\: Verified }}}}}$

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