Question

question 7 6.25 pts
in the diagram ( overline{mp} parallel overline{tr} ), ( mangle pmn = 28^{circ} ),
and ( mangle mnp = 37^{circ} ).
( mangle nrt=) 。

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(\angle MNP=\angle RNT = 37^{\circ}\)

Step2: Use alternate - interior angles property

Since \(MP\parallel TR\), \(\angle PMN=\angle NTR = 28^{\circ}\)

Step3: Use triangle - angle sum property

In \(\triangle NRT\), the sum of interior angles of a triangle is \(180^{\circ}\). Let \(m\angle NRT=x\). Then \(x + 28^{\circ}+37^{\circ}=180^{\circ}\)

$$x=180^{\circ}-(28^{\circ} + 37^{\circ})$$

$$x=180^{\circ}-65^{\circ}$$

$$x = 115^{\circ}$$

Answer:

\(115\)