Question 51

In $$\triangle PQR, \angle Q > \angle R, PS$$ is the bisectors of $$\angle P$$ and $$PT \perp PQ$$. If $$\angle SPT = 28^\circ$$ and $$\angle  R = 23^\circ$$, then the measure of $$\angle Q$$ is: 

Solution

$$\angle SPT = \frac{1}{2}(\angle Q - \angle R)$$
28 $$\times 2 = \angle Q - 23$$
$$angle Q = 56 + 23 = 79\degree$$


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