Question

If m< BCD = 54, find m< BAC

Answer 1

m∠BAC = 27°

Solution:

ABCD is a quadrilateral.

AB and CD are parallel lines.

Given m∠BCD = 54°

AC bisect ∠BCD.

m∠DCA + m∠CAB = m∠BCD

m∠DCA + m∠DCA = 54°   (since ∠ACB = ∠DCA)

2 m∠DCA  = 54°

Divide by 2 on both sides, we get

m∠DCA  = 27°

AB and CD are parallel lines and AC is the transversal.

If two parallel lines cut by a transversal, then the alternate interior angles are equal.

m∠BAC = m∠DCA

m∠BAC = 27°

Hence m∠BAC = 27°.