Question

Let angle 1 and angle 2 be complementary. If má 1 = 4x +3 and m42 = x + 2, find the measure

of angle 1.

Answer 1

m∠1 = 71°

Explanation:

Angle 1 and 2 are complementary, meaning the measures of the two angles add up to 90°.

Set the measures of the two angles equal to 90°

`(4x+3)+(x+2)=90\\`

Combine like terms

`5x+5=90`

Solve for x

`x=17`

Plug the value of 'x' back into the given equation for the measure of angle 1

`m<1 = 4x+3\\m<1 = 4(17)+3\\`

m∠1 = 71°

Answer 2

Explanation:

Complimentary angles are two acute angles whose sum is 90 degrees.

Angle 1 = 4x + 3

Angle 2 = x + 2

Since angle 1 and angle 2 are complimentary angles, it means that

4x + 3 + x + 2 = 90

4x + x + 5 = 90

Subtracting 5 from the left hand side and the right hand side of the equation, it becomes

5x + 5 - 5 = 90 - 5

5x = 85

Dividing the left hand side and the right hand side of the equation by 5, it becomes

5x/5 = 85/5

x = 17

The measure of angle 1 would be

4 × 17 + 3 = 68 + 3 = 71 degrees