Question

∠Q and ∠R are complementary. The measure of ∠Q is 26° less than the measure of ∠R. Find the measure of each angle.

Answer 1

Answer:

∠Q= 32°

∠R = 58°

EXPLAINATION

GIVEN -

• Q and R are complementary
• ∠Q is 26° less than ∠R

TO FIND -

• Measure of each angle

SOLUTION -

WE know that complementary angles are the angles whose sum is 90°

according the the question,

∠Q + ∠R = 90°

Let ∠R be X

∠Q = X - 26

X + X- 26 = 90°

2x- 26 = 90

2x = 90+ 26

2x= 116

x= 116/2

x= 58°

x- 26 = 58 - 26 = 32°

∠Q = 32°

∠R = 58°

MORE TO KNOW -

• Suplementary angles are the angles whose sum is 180°

• The suplementary angle of 90 is 90°

• The complementary angle of 45 is 45°

Answer 2

Given :- ∠Q and ∠R are complementary. The measure of ∠Q is 26° less than the measure of ∠R.

To Find :- The measure of each angle ?

Concept used :- When two angles are complementary , their sum is equal to 90° .

Solution :-

Since, ∠Q and ∠R are complementary .

So,

→ ∠Q + ∠R = 90° --------- Eqn.(1)

and,

→ ∠R - ∠Q = 26° ----------- Eqn.(2)

adding Eqn.(1) and Eqn.(2) we get,

→ (∠Q + ∠R) + (∠R - ∠Q) = 90° + 26°

→ ∠Q - ∠Q + ∠R + ∠R = 116°

→ 2∠R = 116°

→ ∠R = 58°

putting value of ∠R in Eqn.(1),

→ ∠Q + 58° = 90°

→ ∠Q = 90° - 58°

→ ∠Q = 32°

Verification :-

→ ∠Q + ∠R = 58° + 32° = 90°

→ ∠R - ∠Q = 58° - 32° = 26°

Hence, the measure of ∠Q is equal to 32° and measure of ∠R is equal to 58° .

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