Question

In the following options, the measures of three angles are given. Which of these can form a triangle?
(1) 45°, 61° 73°
(2) 63°, 37°, 80°
(3) 30°, 20°, 1250
(4) 59°, 72°, 61°​

Answer 1

Answer:

Two angles of a triangle are of measures 150° and 30°. Find the measure of the third angle.

Solution:

Let the third angle be x

Sum of all the angles of a triangle = 180°

105° + 30° + x = 180°

135° + x = 180°

x = 180° – 135°

x = 45°

Therefore the third angle is 45°

Answer 2

The options (2) and (4) can form a triangle.

63°, 37°, 80°

59°, 72°, 61°​

To form a triangle, the sum of any two angles must be greater than the third angle. Let's check the given options accordingly:

(1) 45° + 61° = 106° < 73°, so these angles cannot form a triangle.

(2) 63° + 37° = 100° > 80°, 63° + 80° = 143° > 37°, and 37° + 80° = 117° > 63°, so these angles can form a triangle.

(3) The angle 1250 is not possible in a triangle as the sum of all three angles in a triangle is always 180°.

(4) 59° + 61° = 120° > 72°, 59° + 72° = 131° > 61°, and 61° + 72° = 133° > 59°, so these angles can form a triangle.

Therefore, the options (2) and (4) can form a triangle.

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