Exercise 14
The Triangle — Practice
Work each question on paper first, then reveal the model answer. Questions are graded from recall to problem solving.
1. The sum of the measures of the interior angles of a triangle = ____°
2. The measure of the exterior angle of any triangle equals the sum of ____
3. In triangle ABC, if m(∠A) = 70° and m(∠C) = 50°, then m(∠B) = ____°
4. If the three angles of a triangle are equal, each angle measures ____°
5. A triangle has angles (2x + 16)°, (x + 1)° and 82°. Find x.
6. A triangle has angles (15x + 1)°, (6x + 5)° and (4x − 1)°. Find x.
7. Which of these sets can be side lengths of a triangle? (1) 9, 5, 4 cm (2) 7, 6, 5 cm (3) 10, 5, 2 m (4) 10, 6, 5 cm (5) 8, 4, 4 cm (6) 12, 3, 6 cm
8. In triangle ABC, AB = 5 cm and BC = 7 cm. What is the smallest possible integer value of AC?
9. A wire 48 cm long is bent at two points to form a triangle. Can the pieces be (1) 12 cm and 16 cm, or (2) 12 cm and 12 cm?
10. ABC is a triangle whose angle measures are in the ratio 5 : 7 : 8. Find each angle.
11. In the figure, ED ∥ CB with m(∠D) = 100°, m(∠C) = 30° and A ∈ BD. Find m(∠BAC).
12. A car barrier opens through an angle less than 90°; the distance between the barrier's tip in the initial and final positions is 4 m. What is the smallest integer length of the barrier?
13. In triangle ABC, BC = 9 cm. Find the smallest integer perimeter of the triangle.
Multiple Choice Questions
1. If the sum of two angles of a triangle is 130°, the third angle is:
2. In triangle XYZ, m(∠X) = 50° and m(∠Y) = 100°. Then m(∠Z) =
3. Which set can form a triangle?
4. An exterior angle of a triangle measures 120°. One remote interior angle is 45°. The other is: