Question

$\angle 1$ and $\angle 2$ are vertical angles. if $m\angle 1 = (5x + 15)\degree$ and $m\angle 2 = (6x + 6)\degree$, then find the measure of $\angle 1$.

Explanation:

Step1: Recall vertical angles property

Vertical angles are equal, so \( m\angle1 = m\angle2 \).
\[
5x + 15 = 6x + 6
\]

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides:
\[
15 = x + 6
\]
Subtract 6 from both sides:
\[
x = 15 - 6 = 9
\]

Step3: Find \( m\angle1 \)

Substitute \( x = 9 \) into \( m\angle1 = (5x + 15)^\circ \):
\[
m\angle1 = 5(9) + 15 = 45 + 15 = 60^\circ
\]

Answer:

\( 60^\circ \)