Verified answer

To find the measures of the angles in a triangle when given the ratio of their measures, we need to determine the common multiplier for the ratio.

Let's assume the common multiplier is 'x.'

The given ratio is 3:5:7, so the measures of the angles can be represented as 3x, 5x, and 7x.

To find the value of 'x,' we know that the sum of the angles in a triangle is 180 degrees.

Therefore, we can set up the equation:

3x + 5x + 7x = 180

Simplifying the equation, we have:

15x = 180

Dividing both sides of the equation by 15:

x = 180/15

x = 12

Now that we have found the value of 'x,' we can calculate the measures of the angles:

First angle: 3x = 3 * 12 = 36 degrees

Second angle: 5x = 5 * 12 = 60 degrees

Third angle: 7x = 7 * 12 = 84 degrees

Therefore, the measures of the angles in the triangle are 36 degrees, 60 degrees, and 84 degrees.

Answer :

• The angles of triangle is 36°, 60° and 84°.

Given :

• The angles of a triangle are in the ratio 3 : 5 : 7.

To Find :

• The measure of these angles ?

Solution :

• Let the ratio be 3x, 5x and 7x.
• The sum of angles of a triangle are 180° and this property is known as angle sum property.

✧ According to the question :

➤ 3x + 5x + 7x = 180°

➤ 8x + 7x = 180°

➤ 15x = 180°

➤ x = 180°/15

• Multi cancellation

➤ x = 12

• The value of x is 12.

Therefore,

• The first angle is 3x = 3 × 12 = 36°.
• The second angle is 5x = 5 × 12 = 60°.
• The third angle is 7x = 7 × 12 = 84°.

Hence,

• The angles of triangle is 36°, 60°, and 84°.

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V E R I F I C A T I O N :

➤ 36° + 60° + 84° = 180°

➤ 96° + 84° = 180°

➤ 180° = 180°

• LHS = RHS