Question

4(b). Two isosceles triangles PQR and PQS are drawn on opposite sides of a common base PQ. If ∠PQR=66° and ∠PSQ=109°, calculate the value of ∠RQS.

Accepted Answer

Triangle PQR is isosceles on base PQ, with ∠PQR=∠QPR=66° (base angles equal).
Triangle PQS is isosceles on base PQ, with apex ∠PSQ=109°, so base angles ∠PQS=∠QPS=(180−109)/2=35.5°.
Since R and S are on opposite sides of PQ, ∠RQS = ∠PQR + ∠PQS = 66°+35.5° = 101.5°

WAEC Mathematics 2014 Theory — Question 8

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