Question

Can anyone help please right answer only

Answer 1

The value of x is 27°.

Solution:

Given $\triangle \mathrm{ACB} \cong \Delta \mathrm{DCE}$.

∠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°.