Question

in the figure below, $m\angle 1=(x + 32)\degree$ and $m\angle 2 = 3x\degree$. find the angle measures. $m\angle 1=\square\degree$ $m\angle 2=\square\degree$

Explanation:

Step1: Identify angle relationship

∠1 and ∠2 form a linear pair, so \( m\angle1 + m\angle2 = 180^\circ \).
Substitute \( m\angle1 = (x + 32)^\circ \) and \( m\angle2 = 3x^\circ \):
\( (x + 32) + 3x = 180 \)

Step2: Solve for \( x \)

Combine like terms:
\( 4x + 32 = 180 \)
Subtract 32 from both sides:
\( 4x = 180 - 32 = 148 \)
Divide by 4:
\( x = \frac{148}{4} = 37 \)

Step3: Find \( m\angle1 \)

Substitute \( x = 37 \) into \( m\angle1 = (x + 32)^\circ \):
\( m\angle1 = 37 + 32 = 69^\circ \)

Step4: Find \( m\angle2 \)

Substitute \( x = 37 \) into \( m\angle2 = 3x^\circ \):
\( m\angle2 = 3 \times 37 = 111^\circ \)

Answer:

\( m\angle1 = \boldsymbol{69}^\circ \)
\( m\angle2 = \boldsymbol{111}^\circ \)