Question

in the figure below, ( m angle 2 = 56 ^ { circ } ) and ( m angle g f h = 145 ^ { circ } ). find ( m angle 1 ).

Explanation:

Step1: Use the angle - sum property

We know that \(m\angle GFH=m\angle1 + m\angle2\) (by the angle - addition postulate).

Step2: Solve for \(m\angle1\)

Substitute the given values \(m\angle2 = 56^{\circ}\) and \(m\angle GFH=145^{\circ}\) into the equation \(m\angle1=m\angle GFH - m\angle2\).
So, \(m\angle1=145^{\circ}- 56^{\circ}\)

$$m\angle1 = 89^{\circ}$$

Answer:

\(89^{\circ}\)