Question

in the figure below, ( mangle pqs = 74^{circ} ) and ( mangle 2 = 48^{circ} ). find ( mangle 1 ).

Explanation:

Step1: Analyze the relationship between angles

From the figure, we know that \(m\angle PQS=m\angle1 + m\angle2\) (angle - addition - postulate).

Step2: Solve for \(m\angle1\)

We are given that \(m\angle PQS = 74^{\circ}\) and \(m\angle2=48^{\circ}\).
Substitute the given values into the equation \(m\angle1=m\angle PQS - m\angle2\).
So \(m\angle1 = 74^{\circ}-48^{\circ}\).

$$m\angle1=26^{\circ}$$

Answer:

\(26\)