Question

The acute angles of right triangle are in the ratio 2:3. Find the measure of each of these angles.

60° and 30°

36° and 54°

50° and 40°

55° and 35°

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Answer 1

The correct option is 36 degrees and 54 degrees.

The ratios are 2:3 hence total is 5.
Divide 90 degrees by 5 which is equal to 18.
Now multiply 18 with 2 and you get your first angle which is 36 degrees. Multiply 18 with 3 and you get 54 degrees.

Hope this helps.
Have a great day.

Answer 2

Answer :

›»› The measure of each angles of a triangle are 36°, and 54° respectively.

Given :

• The acute angles of right triangle are in the ratio 2:3.

To Find :

• The measure of each of these angles.

Solution :

Let us assume that, the measure of each angles is 2x, and 3x respectively.

As it is given that, the triangle is right angle triangle. So, our three angles are,

→ 2x, 3x, 90.

As we know that

The sum of all three angles of a triangle is 180°.

→ 2x + 3x + 90 = 180

→ 5x + 90 = 180

→ 5x = 180 - 90

→ 5x = 90

→ x = 90 ÷ 5

→ x = 18

Therefore,

The measure of each angles of a triangle will be,

• 2x = 2 * 18 = 36°.
• 3x = 3 * 18 = 54°.

Hence, the measure of each angles of a triangle are 36°, and 54° respectively.

So, option (2) 36° and 54° is correct ✔

Verification :

The sum of all three angles of a triangle is 180°.

→ 36 + 54 + 90 = 180

→ 90 + 90 = 180

→ 180 = 180

Here, LHS = RHS

Hence Verified !