In a $\Delta ABC$,$\angle C = 3 \angle B = 2(\angle A + \angle B)$. Find the three angles.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) Given that,$\angle C = 3 \angle B = 2(\angle A + \angle B)$.
From $3 \angle B = 2(\angle A + \angle B)$,we get $3 \angle B = 2 \angle A + 2 \angle B$,which simplifies to $\angle B = 2 \angle A$,or $2 \angle A - \angle B = 0 \dots (i)$.
We know that the sum of the angles in a triangle is $180^{\circ}$,so $\angle A + \angle B + \angle C = 180^{\circ}$.
Since $\angle C = 3 \angle B$,we substitute this into the sum: $\angle A + \angle B + 3 \angle B = 180^{\circ}$,which gives $\angle A + 4 \angle B = 180^{\circ} \dots (ii)$.
Multiplying equation $(i)$ by $4$,we get $8 \angle A - 4 \angle B = 0 \dots (iii)$.
Adding equations $(ii)$ and $(iii)$,we get $9 \angle A = 180^{\circ}$,which implies $\angle A = 20^{\circ}$.
Substituting $\angle A = 20^{\circ}$ into equation $(ii)$,we get $20^{\circ} + 4 \angle B = 180^{\circ}$,so $4 \angle B = 160^{\circ}$,which gives $\angle B = 40^{\circ}$.
Finally,$\angle C = 3 \angle B = 3 \times 40^{\circ} = 120^{\circ}$.
Thus,the angles are $\angle A = 20^{\circ}$,$\angle B = 40^{\circ}$,and $\angle C = 120^{\circ}$.

Explore More

Similar Questions

Solve the following pair of equations by the method of cross multiplication:
$\frac{x}{a} + \frac{y}{b} = 2$
$ax - by = a^{2} - b^{2}$

Difficult
View Solution

$A$ pair of linear equations which has a unique solution $x=2, y=-3$ is

$A$ two-digit number is such that the product of its digits is $10$. When $27$ is added to the original number,the new number obtained is the same as the number obtained by interchanging the digits of the original number. Determine the number.

Which of the following is a solution of the linear equation in two variables $x - 2y = 4$?

The cost of $2\,kg$ of apples and $1\,kg$ of grapes on a day was found to be Rs. $160$. After a month,the cost of $4\,kg$ of apples and $2\,kg$ of grapes is Rs. $300$. Represent this situation as a pair of linear equations in two variables.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo