Q. 1 A3.7( 12 Votes )

# 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°.

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