Question

1. ( mangle ghr = 22^circ ) and ( mangle rhi = 130^circ ). find ( mangle ghi ).

Explanation:

Step1: Identify angle addition

To find \( m\angle GHI \), we use the angle addition postulate, which states that if a point \( R \) lies in the interior of \( \angle GHI \), then \( m\angle GHI = m\angle GHR + m\angle RHI \).

Step2: Substitute the given values

We know \( m\angle GHR = 22^\circ \) and \( m\angle RHI = 130^\circ \). Substituting these values into the formula:
\( m\angle GHI = 22^\circ + 130^\circ \)

Step3: Calculate the sum

Adding the two angles: \( 22^\circ + 130^\circ = 152^\circ \)

Answer:

\( 152^\circ \)