Question

Measures of angles of a triangle are in the ratio 11 :3:4 then the measure of the greatest angle is *in​

Answer 1

✪ Question ✪

Measures of angles of a triangle are in the ratio 11:3:4, then the measure of the greatest angle is?

✪ Given ✪

Measures of angles of a triangle are in the ratio 11:3:4.

✪ To find ✪

The measure of the greatest angle.

✪ Solution ✪

Let the angles are 11x°, 3x° and 4x°.

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

∴ 11x + 3x + 4x = 180

⇒18x = 180

⇒x = 180/18

⇒x = 10

✪ Hence ✪

x = 10

11x° = (11 × 10)° = 110°

3x° = (3 × 10)° = 30°

4x° = (4 × 10)° = 40°

✪ Therefore ✪

The measure of the largest angle is 110°.

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✪ Verification ✪

11x + 3x + 4x = 180

⇒110 + 30 + 40 = 180

⇒180 = 180

So, L.H.S = R.H.S.

Hence, verified.

๑ Hope this helps you. ๑