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\\\\(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+(1)/(2)x+2x+5=180\ \ \ \ |-5\\\\3(1)/(2)x=175\\\\3.5x=175\ \ \ \ |:3.5\\\\\boxed{x=50}`

`m\angle A=50^o\\\\m\angle B=(1)/(2)\cdot50^o=25^o\\\\m\angle C=2\cdot50^o+5=105^o`