Question

In a triangle ABC, $\angle$A + $\angle$B = ${144}^{\circ }$ and $\angle$A + $\angle$C = ${124}^{\circ }$.
Calculate each angle of the triangle.

• A. A = ${88}^{\circ }$, B = ${56}^{\circ }$ and C = ${36}^{\circ }$
• B. A = ${78}^{\circ }$, B = ${66}^{\circ }$ and C = ${36}^{\circ }$
• C. A = ${58}^{\circ }$, B = ${86}^{\circ }$ and C = ${36}^{\circ }$
• D. A = ${88}^{\circ }$, B = ${26}^{\circ }$ and C = ${66}^{\circ }$

Answer 1

The correct option is A A = ${88}^{\circ }$, B = ${56}^{\circ }$ and C = ${36}^{\circ }$

$\angle A+\angle B=144$ ...(I)
$\angle A+\angle C=124$....(II)
Add, the two equations,
$\angle A+\angle B+\angle C+\angle A=144+124$
Sum of angles of triangle = 180
$180+\angle A=268$
$\angle A={88}^{\circ }$
From equation I,
$\angle B=144-88={56}^{\circ }$
From equation II,
$\angle C=124-88={36}^{\circ }$