Question

if two acute angles of a right triangle are equal, then each acute angle is equal to what

Answer 1

Answer:

Step-by-step explanation:

Since we have a right triangle, then

the sum of the acute angles is 90°

and since both of them are equal

each one is equal to 90°/2 = 45°.

Answer 2

Answer:

Each acute angle is equal to 45°

Step-by-step explanation:

Given,

Two acute angles of  a right-angled triangle are equal

Recall the concepts

• A right-angled triangle is a triangle in which one angle is equal to 90degrees
• The sum of three angles of a triangle is equal to 180 degrees

Solution:

Let ABC be the triangle.

Let ∠A, ∠B, ∠and C are the three angles of the triangle

Since the ΔABC is a right-angled triangle, one angle is equal to 90°.

Let us take ∠A = 90°

Also given the two acute angles of the triangle are equal, hence we have

∠B = ∠C

Since the sum of three angles of a triangle is equal to 180°, we get

∠A +∠B + ∠C = 180

Substituting the value of ∠A, ∠B

90 + ∠C + ∠C = 180

90 +2∠C = 180

2∠C = 90

∠C = 45°

∠B = 45°

∴ Each acute angle is equal to 45°

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