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°