Congruent triangles

Question

Triangle ABC≅Triangle UVW: Angle B is 7x + 6 degrees. Angle C is 4x + 10 degrees. Angle U is 5x + 4. What is the value of X? What are the exact measures of each of the 6 angles?

Answer 1

Since ΔABC ≅ ΔUVW, then ∠A ≅ ∠U. For ΔABC:

m∠A + m∠B + m∠C = 180º

Since ∠A ≅ ∠U, we can substitute ∠U for ∠A:

m∠U + m∠B + m∠C = 180º

5x+4 + 7x+6 + 4x+10 = 180

Solve for x. The six angles are:

m∠A = m∠U = 5x+4

m∠B = m∠V = 7x+6

m∠C = m∠W = 4x + 10

Plug in the value you got for x to compute the answers. The units are degrees.