Question

If triangle ABC is congruent to triangle PQR,angle A=50°,angle Q=60° then prove that angleR=70°.​

Answer 1

here
ABC congruent PQR
therefore
A=P,B=Q,C=R
A=50°,Q=60°

measure of triangle is 180°
P+Q+R=180
50+60+R=180
110+R=180
R=180-110
R=70°

this prove

Answer 2

Given,

∆ABC congruent to ∆PQR

Angle A = 50°

Angle Q = 60°

To prove,

The measure of angle R = 70°.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the measure of angle R is equal to x°.

Mathematically,

Sum of all the angles of any triangle = 180°

{Statement-1}

According to the question;

∆ABC congruent to ∆PQR

=> By CPCT (Corresponding parts of congruent triangles), we get;

angle A = angle P

angle B = angle Q

angle C = angle R

{Equation-1}

Now, according to the equation-1;

angle A = angle P = 50°

angle B = angle Q = 60°

angle C = angle R = x°

Now, according to statement-1;

In ∆PQR,

Angle P + angle Q + angle R = 180°

=> 50° + 60° + x = 180°

=> x = 70°

=> measure of angle R = 70°

Hence, it is proved that the measure of angle R is equal to 70°.