Theory question 105
Angles and Polygons(a) In the diagram, MN||ST, NP||QT and ∠STQ = 70°. Find x.
(b) In the diagram, AC is a straight line, |BC| = |BD|, ∠BCD = 50° and ∠BAD = 55°. Find ∠BDA.
Show the model answer
Model answer
(a) MN ∥ ST and NP ∥ QT, but NP points the opposite way to TQ, so ∠MNP and ∠STQ add up to 180°.
x = 180° − 70° = 110°.
(b) BC = BD, so ∠BDC = ∠BCD = 50° and ∠CBD = 180 − 100 = 80°.
∠CBD is an exterior angle of triangle ABD: 80° = 55° + ∠BDA, so ∠BDA = 25°.
Explanation
An exterior angle of a triangle equals the sum of the two opposite interior angles.