Question

in the figure below, m∠1 = (x - 18)° and m∠2 = 8x°. find the angle measures. m∠1 = ☐° m∠2 = ☐°

Explanation:

Step1: Identify angle relationship

∠1 and ∠2 form a linear pair, so \( m\angle1 + m\angle2 = 180^\circ \).
Substitute \( m\angle1=(x - 18)^\circ \) and \( m\angle2 = 8x^\circ \):
\( (x - 18)+8x = 180 \)

Step2: Solve for \( x \)

Combine like terms: \( 9x - 18 = 180 \)
Add 18 to both sides: \( 9x = 198 \)
Divide by 9: \( x = 22 \)

Step3: Find \( m\angle1 \)

Substitute \( x = 22 \) into \( m\angle1=(x - 18)^\circ \):
\( m\angle1=(22 - 18)^\circ = 4^\circ \)

Step4: Find \( m\angle2 \)

Substitute \( x = 22 \) into \( m\angle2 = 8x^\circ \):
\( m\angle2 = 8\times22^\circ = 176^\circ \)

Answer:

\( m\angle1 = \boxed{4}^\circ \)
\( m\angle2 = \boxed{176}^\circ \)