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

Step-by-step explanation:

1. let the two congruent angles of =x

2. given angle =90*

3. A.T.Q

by angle sun property

90+x+x=180*

90+2x=180

2x= 180- 90=90

2x=90

x=90÷2

x=45

Answer 2

Answer: Each angle will be 45°, So one angle will measure 45°

Step-by-step explanation:

We are told that there's a triangle with a measure of 90° that means its a right angled triangle. We are also told that the other two interior angles are congruent. We are told to explain how to find the measure of one of the two congruent angles.

• We know that the sum of the all the angles in a triangle is 180°
• We know that if two angles are congruent it means they have the same measure.

Using the above two hints, we will find the measure of one of the congruent angles.

So, let the triangle be ABC right angled at B.

We know that, B = 90°

Since, we don't know A and C we will take both the angles as x (Since both are congruent)

So By Angle sum property: ∠A + ∠B +C = 180°

x + 90 + x = 180°

Now we will solve for x

2x = 180 - 90

2x = 90

x = 90/2

x = 45°

Therefore, x = 45° so each of the congruent angles will measure 45° hence satisfying the angle sum property.

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