Question

1. in the given figure, m∠p = 56° and m∠q= 82°. find m∠qrx.

Explanation:

Step1: Recall the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In triangle \(PQR\), \(\angle QRX\) is an exterior angle at vertex \(R\), and the two non - adjacent interior angles are \(\angle P\) and \(\angle Q\).

Step2: Calculate \(m\angle QRX\)

We know that \(m\angle P = 56^{\circ}\) and \(m\angle Q=82^{\circ}\). By the exterior angle theorem, \(m\angle QRX=m\angle P + m\angle Q\).
Substitute the given values: \(m\angle QRX = 56^{\circ}+82^{\circ}\)
\(m\angle QRX=138^{\circ}\)

Answer:

\(138^{\circ}\)