Find ‘x’ in the following figures?

Given: In Δ ABC, m∠ A = 56° and m∠ B = x°

m∠ ACD is the exterior angle of the Δ ABC.

m∠ ACD = 123°

In Δ ABC,

m∠ B + m∠ A + m∠ ACB = 180° (Sum of the measures of all angles of a triangle

is 180°)

⇒ x° + 56° + m∠ ACB = 180° (1)

m∠ ACB + m∠ ACD = 180° (Linear pair of angles)

⇒ m∠ ACB + 123° = 180° (2)

From (1) and (2), we get,

x° + 56° + m∠ ACB = m∠ ACB + 123°

⇒ x° + 56° = m∠ ACB + 123° - m∠ ACB (Transposing

m∠ ACB to RHS)

x° + 56° = 123°

⇒ x = 123 – 56 (Transposing 56 to RHS)

x = 67

∴ The value of x is 67°.