Question

PQRS is a Parallelogram. RT and Qt are bisectors of angle R and Q respectively meeting at T. find the measure of angle T

Answer 1

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Answer 2

The measure of ∠ T is 90°.

Step-by-step explanation:

Given:

PQRS is a Parallelogram. RT and Qt are bisectors of angle R and Q respectively meeting at T.

Since ABCD is Parallelogram.

So, angle A +angle D=180   [co-interior angles]

Multipying by $\frac{1}{2}$ on both the sides

$\frac{1}{2}( \angle Q+\angle R)=\frac{1}{2}\times 180$

$\frac{1}{2}\angle Q+\frac{1}{2}\angle R= 90$

Now in triangle QRT,

$\angle Q+\angle R+\angle T=180\°$

$90\°+\angle T=180\°$

$\angle T= 180\°-90\°$

Hence $\angle T=90\°$