Question

in the figure below, $m\angle 1 = 7x^\circ$ and $m\angle 2 = (x - 12)^\circ$. find the angle measures.\
\
$m\angle 1 = \square^\circ$\
$m\angle 2 = \square^\circ$

Explanation:

Step1: Identify angle relationship

Angles 1 and 2 form a linear pair, so \( m\angle1 + m\angle2 = 180^\circ \).
Substitute \( m\angle1 = 7x^\circ \) and \( m\angle2 = (x - 12)^\circ \):
\( 7x + (x - 12) = 180 \)

Step2: Solve for \( x \)

Simplify the equation:
\( 7x + x - 12 = 180 \)
\( 8x - 12 = 180 \)
Add 12 to both sides:
\( 8x = 180 + 12 \)
\( 8x = 192 \)
Divide by 8:
\( x = \frac{192}{8} = 24 \)

Step3: Find \( m\angle1 \)

Substitute \( x = 24 \) into \( m\angle1 = 7x^\circ \):
\( m\angle1 = 7 \times 24 = 168^\circ \)

Step4: Find \( m\angle2 \)

Substitute \( x = 24 \) into \( m\angle2 = (x - 12)^\circ \):
\( m\angle2 = 24 - 12 = 12^\circ \)

Answer:

\( m\angle1 = \boxed{168}^\circ \)
\( m\angle2 = \boxed{12}^\circ \)