The value of x is 27°.
Solution:
Given
.
∠A = 3x – 10, ∠C = 45°, ∠D = 2x + 10
If two triangles are congruent, then the angles are congruent.
∠A = ∠E (Alternate interior angles)
∠C = ∠C (Reflexive property)
∠B = ∠D (Alternative interior angles)
⇒ ∠B = 2x + 10
Sum of the interior angles of the triangle = 180°
In ΔACB,
3x – 10 + 45° + 2x + 10 = 180°
5x + 45° = 180°
Subtract 45° on both sides of the equation.
5x = 135°
Divide by 5 on both sides of the equation.
x = 27°
The value of x is 27°.