Question

answer attempt 1 out of 2

( g=square^{circ} )
( k=square^{circ} )
( h=square^{circ} )
( m=square^{circ} )

Explanation:

Step1: Vertical angles

Vertical angles are equal. So, \(h = 63^{\circ}\) (because \(h\) and the \(63^{\circ}\) angle are vertical angles).

Step2: Linear - pair

A linear - pair of angles sum to \(180^{\circ}\). For \(g\) and \(h\), since \(g + h=180^{\circ}\) (linear - pair), and \(h = 63^{\circ}\), then \(g=180^{\circ}-h\). So, \(g = 180 - 63=117^{\circ}\).

Step3: Vertical angles

For \(k\) and \(29^{\circ}\), since \(k\) and \(29^{\circ}\) are vertical angles, \(k = 29^{\circ}\).

Step4: Linear - pair

For \(m\) and \(29^{\circ}\), since \(m + 29^{\circ}=180^{\circ}\) (linear - pair), then \(m=180 - 29 = 151^{\circ}\).

Answer:

\(g = 117^{\circ}\), \(h = 63^{\circ}\), \(k = 29^{\circ}\), \(m = 151^{\circ}\)