ACT Preparation / Unit 13 ACT 1211 worked example, 60 to 90 seconds
Finding Angles in a Triangle Figure
The idea
Angle problems inside a triangle figure are solved in three steps. First, record every given angle and every marked equal side. Second, apply the facts that create new angles: the angle sum, the exterior angle, the base angles of an isosceles triangle, and straight lines. Third, chain them until the asked-for angle appears, writing each step with its reason.
In practice
Worked example: in triangle ABC, AB = AC, and angle A is 36°. Side BC is extended past C to a point D. Find angle ACD. The base angles B and C are equal: (180 − 36)/2 = 72° each. Angle ACD is the exterior angle at C, so it equals angle A plus angle B: 36 + 72 = 108°. Check with the straight line: 180 − 72 = 108°.
Where people slip
Mark which sides are equal before naming base angles: here AB = AC, so the equal angles are B and C, not A.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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