Question

1. ∠1 and ∠2 are vertical angles. if m∠1=(5x + 12)° and m∠2=(6x - 11)°, find m∠1.

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. So, $m\angle1 = m\angle2$.
$5x + 12=6x - 11$.

Step2: Solve for $x$

Subtract $5x$ from both sides of the equation:
$5x+12 - 5x=6x - 11-5x$.
$12=x - 11$.
Then add 11 to both sides:
$12 + 11=x-11 + 11$.
$x = 23$.

Step3: Find $m\angle1$

Substitute $x = 23$ into the expression for $m\angle1$:
$m\angle1=5x + 12$.
$m\angle1=5\times23+12$.
$m\angle1 = 115+12$.
$m\angle1=127^{\circ}$.

Answer:

$127^{\circ}$