Question

in the figure below, ( m angle 1 = 2x^circ ) and ( m angle 2 = (x + 63)^circ ). find the angle measures.
( m angle 1 = square^circ )
( m angle 2 = square^circ )

Explanation:

Step1: Identify angle relationship

∠1 and ∠2 are supplementary (form a straight line), so \(2x + (x + 63) = 180\).

Step2: Solve for \(x\)

Simplify: \(3x + 63 = 180\). Subtract 63: \(3x = 117\). Divide by 3: \(x = 39\).

Step3: Find \(m\angle1\)

Substitute \(x = 39\) into \(2x\): \(2(39) = 78\).

Step4: Find \(m\angle2\)

Substitute \(x = 39\) into \(x + 63\): \(39 + 63 = 102\).

Answer:

\(m\angle1 = 78^\circ\)
\(m\angle2 = 102^\circ\)