Let’s solve each problem step by step. We’ll use the key rule:
The angles in any triangle add up to 180°. Also, for exterior angles (angles outside the triangle), we can use:
exterior angle = sum of the two opposite interior angles, or sometimes just subtract from 180° if it’s on a straight line.
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Section A
1) Triangle with angles 100°, 30°, and a°
→ 100 + 30 + a = 180
→ 130 + a = 180
→ a = 50
2) Triangle with angles 50°, 45°, and b°
→ 50 + 45 + b = 180
→ 95 + b = 180
→ b = 85
3) Right-angled triangle (one angle is 90°), another is 60°, find c°
→ 90 + 60 + c = 180
→ 150 + c = 180
→ c = 30
4) Isosceles triangle (two sides equal → two base angles equal). Top angle is 34°, so base angles are both d°
→ d + d + 34 = 180
→ 2d = 146
→ d = 73
5) Isosceles triangle with one angle 26°, and the other two equal? Wait — look at markings: two sides have same tick marks → those are the equal sides → so the angles opposite them are equal. The 26° is at the bottom left, and the side opposite it has no mark. The two marked sides are the legs → so the base angles are equal? Actually, let’s check: the angle labeled e° is at the top right, and the side opposite it is the base (no mark). The two marked sides are adjacent to the 26° angle and the e° angle? Hmm — better way: total angles = 180. If two sides are equal, then two angles are equal. Which ones? The two angles that are NOT between the equal sides? Actually, standard: angles opposite equal sides are equal. So if two sides are marked equal, their opposite angles are equal. In this diagram, the two sides with ticks are the ones forming the angle at the bottom left (26°) and the top right (e°)? No — actually, looking again: the triangle has one angle 26°, and two sides marked equal — meaning the two angles opposite those sides are equal. But which sides are marked? The two sides that meet at the vertex with angle e°? Or not? Let me think differently.
Actually, in diagram 5: it's an isosceles triangle with the two equal sides being the ones that form the angle at the
Parent Tip: Review the logic above to help your child master the concept of find the missing angle of a triangle worksheet.
