Question

1. for each diagram below, solve for x. explain what angle properties or relationship(s) you used for each problem.

a.
b.

Explanation:

Step1: Identify angle - relationship in part a

The two angles are complementary, so their sum is 90°.
$6x+(4x + 10)=90$

Step2: Simplify the equation in part a

Combine like - terms:
$6x+4x+10 = 90$
$10x+10 = 90$

Step3: Solve for x in part a

Subtract 10 from both sides:
$10x=90 - 10$
$10x=80$
Divide both sides by 10:
$x = 8$

Step4: Identify angle - relationship in part b

The two angles are supplementary, so their sum is 180°.
$(5x + 13)+(3x+7)=180$

Step5: Simplify the equation in part b

Combine like - terms:
$5x+3x+13 + 7=180$
$8x+20 = 180$

Step6: Solve for x in part b

Subtract 20 from both sides:
$8x=180 - 20$
$8x=160$
Divide both sides by 8:
$x = 20$

Answer:

a. $x = 8$ (using the property of complementary angles, where the sum of two angles is 90°)
b. $x = 20$ (using the property of supplementary angles, where the sum of two angles is 180°)