Question

Given Δ ABC ≅ Δ EFG, What is the value of x?

A. x= 45 °
B. x= 50 °
C. x= 85 °
D. x= 135 °

Answer 1

m<A = 50

m<C = m<G = 85

m<A + m<B +m<C = 180

50 + x + 85 = 180

x + 135 = 180

x = 45

Answer: A. x= 45°

Answer 2

Answer:  The correct option is (A) 45.

Step-by-step explanation:  We are given that triangles ABC and EFG are congruent to each other, where

$m\angle A=50^\circ,m\angle G=85^\circ,m\angle B=x^\circ.$

We are to find the value of x.

We know that the corresponding angles of congruent triangles have equal measures.

So, m∠A = m∠E, m∠B = m∠F and m∠C = m∠G.

Also, since the sum of three angles of a triangle is 180 degrees, so from triangle ABC, we get

$m\angle A+m\angle B+m\angle C=180^\circ\\\\\Rightarrow 50^\circ+85^\circ+x^\circ=180^\circ\\\\\Rightarrow 135^\circ+x^\circ=180^circ\\\\\Rightarrow x^\circ=180^\circ-135^\circ\\\\\Rightarrow x^\circ=45^\circ\\\\\Rightarrow x=45.$

Thus, the required value of x is 45.

Option (A) is CORRECT.