General Aptitude TestQuantitative ReasoningGeometry

If triangles ABC and PQR are both isosceles with AB=AC and PQ=PR, res…

If triangles ABC and PQR are both isosceles with AB=AC and PQ=PR, respectively. If also AB=PQ and BC=QR and angle B=50°, then what is the measure of angle R?

Answer & explanation

Correct answer: option 1

We are given that :- AB = AC , PQ = PR & AB = PQ , BC = QR

In triangle ABC and triangle PQR

AB = PQ

BC = QR

AC = PR

So, by using ( side - side - side ) congruency equation.

△ ABC $≅ △ PQR$

$So, ∠ABC = ∠ PQR$

$\Rightarrow ∠ PQR = 50º$

$And we are given that PQ =PR$

${ In a triangle , angle made by same sides are same }$

$∠ PQR = ∠ PRQ$

$\Rightarrow 50º$