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Think and Answer

Read the following questions and answer them.
1. Can you have a triangle with two obtuse angles?
2. Can you have a triangle with two right angles?
3. Can you have a triangle with two acute angles?

Example 5: Find the missing angles in the following figures.
(a) A (b) A

50° ?

? 60° 45° 80°
B C B C
Solution: (a) ∠A = 50°, ∠C = 60° and ∠B = ?
We know that the sum of the all three interior angles of triangle is equal to 180°.
∠A + ∠B + ∠C = 180°

50° + ∠B + 60° = 180°
∠B + 110° = 180°
∠B = 180° – 110°
∠B = 70°
(b) ∠A = ?, ∠B = 45° and ∠C = 80°

We know that the sum of the all three interior angles of triangle is equal to 180°.
∠A + ∠B + ∠C = 180°
∠A + 45° + 80° = 180°
∠A + 125° = 180°

∠A = 180° – 125°
∠A = 55°
Example 6: The angles of a triangle are in the ratio 2 : 3 : 4. Find the angles.
Solution: Let the angles be 2x, 3x, and 4x.
We know that the sum of the interior angles of a triangle is 180°.

2x + 3x + 4x = 180°
9x = 180°
x = 20°
Therefore, 2x = 2 × 20° = 40°; 3x = 3 × 20° = 60°; 4x = 4 × 20° = 80°
70°
Thus, the angles of the triangle are 40°, 60° and 80°.
Example 7: Find the measure of each angle in the given triangle. y
Solution: In the given triangle,

y = 70° (Vertical opposite angles) x x
Since, the sum of the interior angles of a triangle is 180°.

177 The Triangle and Its Properties