Question

An angle measures 32° more than the measure of its complementary angle. What is the measure of each angle?

Answer 1

Given :

• Measure of an angle is 32° more than the measure of it's complementary angle.

To Find :

• The measure of each angle

Solution :

Let ,

• One of the complementary angles be "x" . Then the other angle becomes " (x + 32)° " {given condition}

Now ,

• Sum of these two angles is equal to 90° . Since they are complementary angles

→ x + x + 32 = 90°

→ 2x + 32 = 90°

→ 2x = 90° - 32°

→ 2x = 58°

→ x = 58°/2

→ x = 29°

Then ,

• x = 29°

• (x + 32) = 29° + 32° = 61°

Hence ,

• The measures of the two given angles is 29° and 61°

Answer 2

Step-by-step explanation:

$\sf Given = \begin{cases} \sf{The\ measure\ of\ an\ angle\ is\ 32⁰\ which\ is\ more\ than\ the\ measure\ of\ its\ complementary\ angle.} \end{cases}$

To find:- We have to find the measure of each angle ?

__________________

☯️ Let one of the complementary angle be x, and then the other angle be (x + 2) according to the given condition.

__________________

● The sum of these two angles is 90⁰ because they made a complementary angle .

$\frak{\underline{\underline{\dag According\ to\ the\ question:-}}}$

$\sf : \implies {x\ +\ x\ +\ 32\ =\ 90⁰} \\ \\ \sf : \implies {2x\ +\ 32\ =\ 90⁰} \\ \\ \sf : \implies {2x\ =\ 90⁰\ -\ 32⁰} \\ \\ \sf : \implies {2x\ =\ 58⁰} \\ \\ \sf : \implies {x\ =\ \cancel \dfrac{58⁰}{2}} \\ \\ \sf : \implies {\purple{\boxed{\bf x\ =\ 29⁰.}}}\bigstar$

● The value of x is 29⁰.

Here:-

$\sf : \implies {x\ =\ 29⁰.}$

$\sf : \implies {(x\ +\ 32)\ =\ 29⁰\ +\ 32⁰\ =\ 61⁰.}$

Hence:-

$\sf \therefore {\underline{The\ measure\ of\ the\ two\ given\ angles\ is\ 29⁰\ and\ 61⁰.}}$