Question

Construct triangle PQR such that PQ =7.9 cm, angle RPQ=30 degrees and angle PQR=120 degrees. The bisector of angle PQR meets PR at M. Measure PM and RM.

Answer 1

Answer:

Third angle = 90° and pqr is an isosceles triangle.

Step-by-step explanation:

In Δ pqr,

∠rpq = 45° , ∠rqp = 45°

Now, Using angle sum property of a triangle which states that sum of all the angles of a triangle is 180°. We get,

∠rqp + ∠rpq + ∠prq = 180°

45° + 45° + ∠prq = 180°

⇒ ∠prq = 90°

Since the two angles :  ∠rqp and ∠rpq are equal. So, the opposite sides to both the angles are also equal ⇒ pr = qr

Now, In Δpqr the two sides are equal, so Δpqr is an isosceles triangle.