Triangles - Properties & Congruence for Competitive Exams

Triangles - Properties and Congruence - Problems on Circles - Applications

Q. If two angles of a triangle are 50° and 60°, what is the measure of the third angle?

Solution

The sum of the angles in a triangle is 180°. Therefore, the third angle is 180 - 50 - 60 = 70°.

Correct Answer: B — 80°

Q. If two triangles have sides in the ratio 3:4, what is the ratio of their areas?

Solution

The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. Therefore, (3:4)² = 9:16.

Correct Answer: B — 9:16

Q. In triangle ABC, if angle A = 50° and angle B = 60°, what is angle C?

Solution

The sum of angles in a triangle is 180°. Therefore, angle C = 180° - 50° - 60° = 70°.

Correct Answer: C — 70 degrees

Q. Which of the following triangles is similar to a triangle with angles 30°, 60°, and 90°?

Solution

Triangles are similar if they have the same angles. The triangle with angles 30°, 60°, and 90° is similar to itself.

Correct Answer: A — 30°, 60°, 90°

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