Question

the figure AB = QR, AC = PQ, BC = PR ;

Also ∠A = 50°, ∠B = 60°

a) ∠Q = ………….

b) ∠P = …………..​

Answer 1

Answer:

The measure of $\angle Q$ is 50 and $\angle P$ is 70.

Step-by-step explanation:

Given that

$AB=QR\\AC=PQ\\BC=PR$

Three sides of triangles $\triangle ABC$ and $\triangle PQR$ are equal. So they are congruent triangles. Hence angles opposite to equal sides are equal. That is

$\angle C= \angle P\\\angle A= \angle Q\\\angle B=\angle R$

The value of angle C can be find using the fact that sum of angles of a triangle is 180.

$\angle A+\angle B+\angle C=180\\50+60+\angle C=180\\\angle C=180-110=70$

Thus we have

$\angle P= 70^o\\\angle Q=50^o$

Answer 2

Given:

Two triangles ABC and QPR in which AB = QR, AC = PQ, BC = PR and ∠A = 50°, ∠B = 60°.

To find:

The value of ∠Q and ∠P.

Solution:

As we know that two triangles are congruent by the side-side-side (SSS) rule if their corresponding sides are equal.

So,

As given

AB = QR, AC = PQ, BC = PR

Hence,

Triangles ABC and QRP are congruent triangles by the SSS rule.

Also,

If two triangles are congruent then their corresponding angles are equal. Hence,

∠A = ∠Q

∠B = ∠R

∠C = ∠P

As given,

∠A = 50° and ∠B = 60°

So, ∠Q = 50° and ∠R = 60°

The value of ∠P is obtained by using the sum property of the angles of a triangle according to which the sum of interior angles of a triangle is 180°.

So, in the triangle QRP,

∠Q + ∠R + ∠P = 180°.

50° + 60° + ∠P = 180°

∠P = 180° - 110°

∠P = 70°

Hence,

a) ∠Q = 50°

b) ∠P = 70°