Question

find the value of x. 14. 15. 16.

Explanation:

Step1: Identify angle - relationship in 14

The two angles are vertical angles. Vertical angles are equal. So we set up the equation $2x - 10=90$.
$2x-10 = 90$

Step2: Solve the equation for 14

Add 10 to both sides of the equation: $2x=90 + 10$, so $2x=100$. Then divide both sides by 2: $x=\frac{100}{2}=50$.

Step3: Identify angle - relationship in 15

The two angles are alternate - interior angles. Alternate - interior angles are equal when the lines are parallel. So we set up the equation $2x=120$.
$2x = 120$

Step4: Solve the equation for 15

Divide both sides of the equation by 2: $x=\frac{120}{2}=60$.

Step5: Identify angle - relationship in 16

The two angles are corresponding angles. Corresponding angles are equal when the lines are parallel. So we set up the equation $3x + 15=135$.
$3x+15 = 135$

Step6: Solve the equation for 16

Subtract 15 from both sides: $3x=135 - 15=120$. Then divide both sides by 3: $x=\frac{120}{3}=40$.

Answer:

1. $x = 50$
2. $x = 60$
3. $x = 40$