Question

use the diagram shown. if m∠1=(4x + 2) and m∠3=(5x - 15), what is the value of x?
a 14
b 15
c 16
d 17

Explanation:

Step1: Identify vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, so $m\angle1 = m\angle3$.

Step2: Set up the equation

Set $4x + 2=5x - 15$.

Step3: Solve the equation for x

Subtract $4x$ from both sides: $4x+2-4x=5x - 15-4x$, which gives $2=x - 15$.
Then add 15 to both sides: $2 + 15=x-15 + 15$, so $x = 17$.

Answer:

D. 17