Q. 1 A3.7( 12 Votes )

Find ‘x’ in the following figures?


Answer :

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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