What are the values of m∠ABC, m∠CBF, m∠ABD and m∠DBE in the given figure? Explain or show your work.

m∠ABC = 72°, m∠CBF = 108°, m∠DBE = 18° and m∠ABD = 90°.

Solution:

In the given figure,

m∠ABD = 90° and m∠EBF = 72°

Sum of the angles in a straight line = 180°

⇒ m∠ABD + m∠DBE + m∠EBF = 180°

⇒ 90° + m∠DBE + 72° = 180°

⇒ 162° + m∠DBE = 180°

⇒ m∠DBE = 180° –  162°

⇒ m∠DBE = 18°

By vertical angle theorem,  

m∠ABC = m∠EBF

m∠ABC = 72°

Sum of the angles in a straight line = 180°

⇒ m∠ABC + m∠CBF = 180°

⇒ 72° + m∠CBF = 180°

⇒ m∠CBF = 180° – 72°

⇒ m∠CBF = 108°

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