Question

In a triangle $ABC,\angle A=x^{\circ },\angle B=(3x-2{)}^{\circ }$ and $\angle C=y^{\circ }$ Also,$\angle C-\angle B=9^{\circ }$.

Find all the three angles of the $\Delta ABC$

• A. $\angle A={15}^{\circ },\angle B={53}^{\circ }$ and $\angle C={82}^{\circ }$
• B. $\angle A={25}^{\circ },\angle B={73}^{\circ }$ and $\angle C={82}^{\circ }$
• C. $\angle A={65}^{\circ },\angle B={43}^{\circ }$ and $\angle C={82}^{\circ }$
• D. $\angle A={35}^{\circ },\angle B={93}^{\circ }$ and $\angle C={82}^{\circ }$

Answer 1

Answer: (B)

$\angle A={25}^{\circ },\angle B={73}^{\circ }$ and $\angle C={82}^{\circ }$

$\angle A=x$
$\angle B=3x-2$
$\angle C=y$
Sum of angles of triangle = 180
$\angle A+\angle B+\angle C=180$
$x+3x-2+y=180$
$4x+y=182$....(I)
Also, $\angle C-\angle B=9$
$y-(3x-2)=9$
$y-3x=7$ ....(II)
Subtracting I and II
$4x+y-y+3x=182-7$
$7x=175$
$x=25$
And, $y=7+3x=$ ${82}^{\circ }$
Thus, $\angle A=x={25}^{\circ }$
$\angle B=3x-2=3\times 25-2={73}^{\circ }$
$\angle C=y={82}^{\circ }$