The sum of the measures of angles x and y is 127 degree. If the measure of anglex is 34 more than half the measure of angle y, what is the measure of each angle?

Jun 16, 2017

$x = {65}^{\circ} , y = {62}^{\circ}$

Explanation:

$\text{we can write the following equations from the statements}$

$x + y = 127 \to \left(1\right)$

$x = \frac{1}{2} y + 34 \to \left(2\right)$

$\text{substitute " (2)" into } \left(1\right)$

$\Rightarrow \frac{1}{2} y + 34 + y = 127$

$\Rightarrow \frac{3}{2} y + 34 = 127$

$\text{subtract 34 from both sides}$

$\frac{3}{2} y \cancel{+ 34} \cancel{- 34} = 127 - 34$

$\Rightarrow \frac{3}{2} y = 93$

$\Rightarrow y = \frac{93}{\frac{3}{2}} = 93 \times \frac{2}{3} = 62$

$\text{substitute this value into " (1)" and solve for x}$

$x + 62 = 127 \Rightarrow x = 65$

$\Rightarrow x = {65}^{\circ} \text{ and } y = {62}^{\circ}$

$\textcolor{b l u e}{\text{As a check }} 62 + 65 = 127$

Jun 16, 2017

$x = 65 , y = 62$

Explanation:

Let the measure of angle x be $x$ and angle y be $y$.

We are given two pieces of information:
$x + y = 127$ .........(1)
$x = \frac{y}{2} + 34$ .........(2)

Substituting (2) into (1) gives
$\frac{y}{2} + 34 + y = 127$
$y = 62$

Substituting $y = 62$ into (1) gives
$x + 62 = 127$
$x = 65$

Therefore $x = 65 , y = 62$