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Find the value of m in the diagram


Question

mathematics-18

Find the value of m in the diagram

Options

A) 34°

B) 27°

C) 23°

D) 17°

The correct answer is D.

Explanation:

Δ ABC, A + 153 = 180 (angles on straight line)
< A = 180 - 153 = 27
< B = 2m (vertically opposite angles)
< C = 7m (corresponding ngles)
< A + < B + < C = 180 (sum of int. angles of Δ)
i.e. 27 + 2m + 7m = 180°
9m = 180 - 27
9m = 153
m = \(\frac{153}{9}\)
= 17


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Dicussion (1)

  • Δ ABC, A + 153 = 180 (angles on straight line)
    < A = 180 - 153 = 27
    < B = 2m (vertically opposite angles)
    < C = 7m (corresponding ngles)
    < A + < B + < C = 180 (sum of int. angles of Δ)
    i.e. 27 + 2m + 7m = 180°
    9m = 180 - 27
    9m = 153
    m = \(\frac{153}{9}\)
    = 17

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