Question

answer
x =

°
y =

°
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Explanation:

Step1: Find the value of x

Since the angle between the vertical - line and the slanted line is 34°, and x is complementary to this 34° angle (because the horizontal and vertical lines are perpendicular), we use the property of complementary angles. Complementary angles add up to 90°. So, $x = 90^{\circ}-34^{\circ}$.
$x = 56^{\circ}$

Step2: Find the value of y

The sum of angles around a point is 360°. The right - angle is 90°, and we know the other non - y angle is 34°. Also, y and the 34° angle are supplementary (a straight - line forms 180°). So, $y=90^{\circ}+34^{\circ}$.
$y = 124^{\circ}$

Answer:

$x = 56$
$y = 124$