Question

find the measure of angle 7.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $2x + 126=3x + 138$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $126=x + 138$. Then subtract 138 from both sides: $x=126 - 138=- 12$.

Step3: Find the measure of an adjacent angle

Substitute $x = - 12$ into $2x+126$. We get $2(-12)+126=-24 + 126 = 102$.

Step4: Use linear - pair property

Angle 7 and the angle with measure $2x + 126$ are a linear - pair (sum to 180°). Let the measure of angle 7 be $y$. Then $y+102 = 180$.

Step5: Solve for the measure of angle 7

Subtract 102 from both sides: $y=180 - 102 = 78$.

Answer:

$78$