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:

angle R measures 58 degree

angle Q measures 32 degree

Step-by-step explanation:

Given that angle Q and angle R are complementary.

that means, angleQ + angleR =90 degree

Let angle R be x

Then angle Q( be x-26)

Now,

x+x-26=90

2x=90+26=116

x=58

Answer 2

∠R = 58° and ∠Q = 32°

GIVEN

∠Q and ∠R are complementary.

The measure of ∠Q is 26° less than the measure of ∠R.

TO FIND

Find the measure of each angle.

SOLUTION

We can simply solve the above problem as follows;

We know that the sum of complementary angles is 90°

Therefore,

∠Q + ∠R = 90° (Equation 1)

It is given,

The measure of ∠Q is 26° less than the measure of ∠R

This means,

∠Q = ∠R-26° (Equation 2)

Putting the value of ∠Q from 2 in 1

∠R -26 + ∠R = 90

2∠R - 26 = 90

2∠R = 90+26

∠R = 116/2 = 58°

Putting the value of ∠R in equation 2

∠Q = 58-26 = 32°

Hence, ∠R = 58° and ∠Q = 32°

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