Question

The angles of a triangle are described as follows: Angle A is the largest angle; it's measure is twice the measure of Angle B. The measure of Angle C is 10 more than one-third of Angle B. Find the measures of angle B?

Answer 1

`\bold{\angle B = 51^\circ}`

Explanation:

Given a
`\triangle ABC` such that
`\angle A` is the largest.

`\angle A` is equal twice of
`\angle B`

`\angle C` is 10 more than one third of
`\angle B`

To find:

Measurement of
`\angle B`.

Solution:

Let
`\angle B =x^\circ`

As per question statement:

`\angle A = 2* \angle B=2x^\circ`

`\angle C = (1)/(3)\angle B +10= (1)/(3)x +10 ^\circ`

Using the angle sum property of a triangle i.e. sum of all the three internal angles is equal to
`180^\circ`.

`2x+x+(1)/(3)x+10 = 180\\\Rightarrow (10)/(3)x =170\\\Rightarrow x = 51^\circ`

Therefore, the answer is:

`\bold{\angle B = 51^\circ}`