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
⇒ 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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