Question

in the figure below, ( mangle 1 = 2x^circ ) and ( mangle 2 = (x + 72)^circ ). find the angle measures.
( mangle 1 = square^circ )
( mangle 2 = square^circ )

Explanation:

Step1: Identify angle relationship

∠1 and ∠2 are supplementary (form a straight line), so \( m\angle1 + m\angle2 = 180^\circ \).
Substitute \( m\angle1 = 2x^\circ \) and \( m\angle2 = (x + 72)^\circ \):
\( 2x + (x + 72) = 180 \)

Step2: Solve for \( x \)

Simplify the equation:
\( 3x + 72 = 180 \)
Subtract 72 from both sides:
\( 3x = 180 - 72 = 108 \)
Divide by 3:
\( x = \frac{108}{3} = 36 \)

Step3: Find \( m\angle1 \)

Substitute \( x = 36 \) into \( m\angle1 = 2x^\circ \):
\( m\angle1 = 2(36) = 72^\circ \)

Step4: Find \( m\angle2 \)

Substitute \( x = 36 \) into \( m\angle2 = (x + 72)^\circ \):
\( m\angle2 = 36 + 72 = 108^\circ \)

Answer:

\( m\angle1 = \boldsymbol{72}^\circ \)
\( m\angle2 = \boldsymbol{108}^\circ \)