Question

in the figure below, m∠1=4x° and m∠2=(x−5)°. find the angle measures.

Explanation:

Step1: Identify angle relationship

∠1 and ∠2 are supplementary (form a straight line), so \( m\angle1 + m\angle2 = 180^\circ \).
Substitute \( m\angle1 = 4x^\circ \) and \( m\angle2 = (x - 5)^\circ \):
\( 4x + (x - 5) = 180 \)

Step2: Solve for \( x \)

Combine like terms:
\( 5x - 5 = 180 \)
Add 5 to both sides:
\( 5x = 185 \)
Divide by 5:
\( x = 37 \)

Step3: Find \( m\angle1 \)

Substitute \( x = 37 \) into \( 4x \):
\( m\angle1 = 4(37) = 148^\circ \)

Step4: Find \( m\angle2 \)

Substitute \( x = 37 \) into \( x - 5 \):
\( m\angle2 = 37 - 5 = 32^\circ \)

Answer:

\( m\angle1 = \boldsymbol{148}^\circ \)
\( m\angle2 = \boldsymbol{32}^\circ \)