Question

part 1 - triangle sum theorem
(the sum of the interior angles of a triangle is always 180°.)

1. ∠a = 45°, ∠b = 65°, ∠c =
2. ∠a = 92°, ∠b = 43°, ∠c =
3. ∠a = 80°, ∠b = 70°, ∠c =
4. ∠a = 38°, ∠b = , ∠c = 102°
5. ∠a = , ∠b = 35°, ∠c = 90°

part 2 - exterior angle theorem
(the exterior angle equals the sum of the two non - adjacent interior angles.)

1. ∠1 (exterior) = 120°, ∠2 = 60°, ∠3 =
2. ∠1 (exterior) = 145°, ∠2 = 80°, ∠3 =
3. ∠1 (exterior) = , ∠2 = 40°, ∠3 = 75°
4. ∠1 (exterior) = 110°, ∠2 = , ∠3 = 45°
5. ∠1 (exterior) = 128°, ∠2 = 63°, ∠3 =

Explanation:

Step1: Apply Triangle Sum Theorem

The sum of interior angles of a triangle is \(180^{\circ}\). For questions 1 - 5: \(\angle A+\angle B+\angle C = 180^{\circ}\), so \(\angle C=180^{\circ}-\angle A - \angle B\) (or solve for the missing angle accordingly).

• Question 1: \(\angle C=180^{\circ}-45^{\circ}-65^{\circ}=70^{\circ}\)
• Question 2: \(\angle C=180^{\circ}-92^{\circ}-43^{\circ}=45^{\circ}\)
• Question 3: \(\angle C=180^{\circ}-80^{\circ}-70^{\circ}=30^{\circ}\)
• Question 4: \(\angle B=180^{\circ}-38^{\circ}-102^{\circ}=40^{\circ}\)
• Question 5: \(\angle A=180^{\circ}-35^{\circ}-90^{\circ}=55^{\circ}\)

Step2: Apply Exterior Angle Theorem

The exterior angle equals the sum of the two non - adjacent interior angles. For questions 6 - 10: \(\angle1=\angle2+\angle3\) (or solve for the missing angle accordingly).

• Question 6: \(\angle3=\angle1-\angle2 = 120^{\circ}-60^{\circ}=60^{\circ}\)
• Question 7: \(\angle3=\angle1-\angle2=145^{\circ}-80^{\circ}=65^{\circ}\)
• Question 8: \(\angle1=\angle2+\angle3=40^{\circ}+75^{\circ}=115^{\circ}\)
• Question 9: \(\angle2=\angle1-\angle3=110^{\circ}-45^{\circ}=65^{\circ}\)
• Question 10: \(\angle3=\angle1-\angle2=128^{\circ}-63^{\circ}=65^{\circ}\)

Answer:

1. \(70^{\circ}\)
2. \(45^{\circ}\)
3. \(30^{\circ}\)
4. \(40^{\circ}\)
5. \(55^{\circ}\)
6. \(60^{\circ}\)
7. \(65^{\circ}\)
8. \(115^{\circ}\)
9. \(65^{\circ}\)
10. \(65^{\circ}\)