In the figure, A, B and C lie on a straight line. Triangle ABD is drawn above the line. Angle DAB = p, angle DBA = q, and angle ADB = 2p. Angle DBC = 62°. Find the value of p.
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Worked Solution
Step 1: Angles on a straight line at B sum to 180°.
p + q + 62° = 180°
p + q = 118° … (1)
Step 2: Angle sum of triangle ABD = 180°.
p + q + 2p = 180°
3p + q = 180° … (2)
Step 3: Subtract (1) from (2).
2p = 62°
p = 31°
Verify: q = 87°. Triangle: 31° + 87° + 62° = 180°. ✓
Correct answer: 31°
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