Question

(d) problem 22: (first taught in lesson 31) find m∠tqr. after you enter your answer press go. m∠tqr =

Explanation:

Step1: Draw a line parallel to \(ST\) and \(PR\) through point \(Q\)

Let the line be \(L\). Since \(ST\parallel L\) and \(PR\parallel L\) (by construction), we can use the property of alternate - interior angles.

Step2: Use the angle - addition property

When \(ST\parallel L\), the angle between \(TQ\) and \(L\) is \(45^{\circ}\) (alternate - interior angles). When \(PR\parallel L\), the angle between \(RQ\) and \(L\) is \(35^{\circ}\) (alternate - interior angles).
The measure of \(\angle TQR\) is the sum of these two angles. So, \(m\angle TQR=45^{\circ}+35^{\circ}\)

Answer:

\(80^{\circ}\)