Question 59

The sides $$PQ$$ and $$PR$$ of $$\triangle PQR$$ are produced to points $$S$$ and $$T$$, respectively. The bisectors of $$\angle SQR$$ and $$\angle TRQ$$ meet at $$U$$. If $$\angle QUR = 79^\circ$$, then the measure of $$\angle P$$ is:

Solution

$$\angle QUR = 79^\circ$$
By the property,

$$\angle QUR = 90 - \angle P/2$$
$$\angle P/2 = 90 - 79 = 11$$
$$\angle P = 22\degree$$


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