# In triangle ABC, the measures of angle B is three more than twice the measure of angle A, and the measure of angle C is two more than four times the measure of angle A. How can I find the measure of the angle in a triangle?

Jul 3, 2016

$\hat{A} = {25}^{\circ} , \hat{B} = {53}^{\circ} . \hat{C} = {102}^{2}$

#### Explanation:

The sum of the 3 angles in the triangle$\hat{A} + \hat{B} + \hat{C} = {180}^{\circ}$

In terms of angle A , angles B and C may be expressed as

$\hat{B} = 2 \hat{A} + 3 \text{ and } \hat{C} = 4 \hat{A} + 2$

$\Rightarrow \hat{A} + 2 \hat{A} + 3 + 4 \hat{A} + 2 = {180}^{\circ}$

$\Rightarrow 7 \hat{A} + 5 = 180 \Rightarrow 7 \hat{A} = 180 - 5 = 175$

divide both sides by 7

$\frac{{\cancel{7}}^{1} \hat{A}}{\cancel{7}} ^ 1 = {\cancel{175}}^{25} / {\cancel{7}}^{1} \Rightarrow \hat{A} = 25$

Thus $\hat{A} = {25}^{\circ} , \hat{B} = \left(2 \times 25\right) + 3 = {53}^{\circ}$

and $\hat{C} = \left(4 \times 25\right) + 2 = {102}^{\circ}$

Check: ${25}^{\circ} + {53}^{\circ} + {102}^{\circ} = {180}^{\circ}$