167k views
0 votes
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?

User Jpnavarini
by
8.5k points

1 Answer

4 votes

Answer:


\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}

User Vvo
by
8.1k points

No related questions found