Question

Find x. Give reasons to justify your solution.

b

Lines
AB
and
CD
are straight lines.

Answer 1

x = 28

Explanation:

If AB and CD are the straight lines, sum all the angles formed at a point lying on this line will be 180°.

m∠COE + m∠EOF + m∠FOB + m∠BOD = 180° [Angles at a point O on line AB]

3x + x + (x + 12) + m∠BOD = 180°

m∠BOD = 180° - (5x + 12)

Similarly, m∠AOD + m∠AOC = 180°

152° + m∠AOC = 180°

m∠AOC = 28°

Since, ∠AOC and ∠BOD are the vertical angles,

m∠AOC = m∠BOD

180° - (5x + 12)° = 28°

5x + 12 = 180 - 28

5x = 140

x = 28