Question

In a triangle , angle B is half of angle A. Angle C is 5 more than double angle A. What are the measurements of each angle?

Answer 1

$x=m\angle A\\\\\dfrac{1}{2}x=m\angle B\\\\2x+5=m\angle C$

$\text{We know: the sum of measures of the angles in the triangle}\\\text{is equal}\ 180^o$

$\text{Therefore we have equation}\\\\m\angle A+m\angle B+m\angle C=180^o\\\\x+\dfrac{1}{2}x+2x+5=180\ \ \ \ |-5\\\\3\dfrac{1}{2}x=175\\\\3.5x=175\ \ \ \ |:3.5\\\\\boxed{x=50}$

$m\angle A=50^o\\\\m\angle B=\dfrac{1}{2}\cdot50^o=25^o\\\\m\angle C=2\cdot50^o+5=105^o$