Question

A triangle has a 90° angle, and the other two interior angles are congruent. Explain how to find the measure of one of the two congruent angles.

Answer 1

Answer:

In a right angled triangle, if the two angles are congruent then there is only one possibilty that both the angles are 45degrees

Explanation:

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Answer 2

Given - a right angle triangle with two interior congruent angles.

To find - measure of one of the two congruent angle.

Solution - let the congruent angle of the triangle be x.

congruent angles are the angles that have same measure.

∴congruent angle = x

we know, the sum of the three angles of a triangle is 180°.

right angle of a triangle = 90°

∴ 90° + x + x = 180°

or, 90° + 2x = 180 °

or, 2x = 180° - 90°

or, 2x = 90°

or, x = 90°/2

or, x = 45°

hence, the value of one of the two congruent angle is 45°