PQRS is a kite and Q lies on AB, such that PR is parallel to AB. If angle PQA = 20 degree and angle BQR = 30 degree. Find (i) angle PSR (i) angle SPQ (iii) angle SRQ. [HINT : Diagonal PR bisects angle P as well as angle R]

given: PQRS is a kite and .

.

To Find that: .

solution: 

since PS = PQ and RS = RQ

since the sum of the angles made on the same side of the straight line is 180 deg.

therefore ..........(3)

[alternate interior angles]

[since the diagonals of  a kite intersect at right angle]

now in the triangle POQ;

therefore

in the triangle POS;

[sum of interior angles of a quadrilateral is 360 deg]

hope this helps you.

cheers!!

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