Question

find the measure of the missing angles. answer attempt 1 out of 2 x = ° y = °

Explanation:

Step1: Find y (right angle)

A right angle is \( 90^\circ \), and we see a right angle symbol. Also, the sum of angles around a straight line or in a right - angle - related setup: \( y = 90^\circ \) (since the angle with the right - angle symbol and \( 41^\circ \) and \( y \) form a straight line? Wait, no. Wait, the right - angle symbol means that the angle between the vertical line and the horizontal line (where \( y \) is) is \( 90^\circ \)? Wait, actually, looking at the diagram, the angle between the vertical line, the \( 41^\circ \) angle, and \( x \) and the horizontal lines. Wait, first, for \( y \): the angle with the right - angle symbol (so \( 90^\circ \)), the \( 41^\circ \) angle, and \( y \) should add up to \( 180^\circ \) (since they are on a straight line). Wait, no, the right - angle symbol is a square, so that angle is \( 90^\circ \). So \( 41^\circ+90^\circ + y=180^\circ \)? No, wait, the horizontal line and the vertical line are perpendicular, so the angle between them is \( 90^\circ \). Wait, actually, the angle \( y \): looking at the diagram, the three angles \( 41^\circ \), the right angle (\( 90^\circ \)), and \( y \) are on a straight line, so their sum is \( 180^\circ \). So \( 41 + 90+y=180 \). But wait, no, the right angle is between the vertical and horizontal, so \( y \) is a right angle? Wait, no, maybe I misread. Wait, the horizontal line and the vertical line are perpendicular, so the angle between them is \( 90^\circ \). Then, the angle \( x \) and \( 41^\circ \) are complementary to the right angle? Wait, no. Let's start with \( y \). The angle \( y \) is a right angle? Wait, the diagram has a right - angle symbol, so \( y = 90^\circ \)? Wait, no, maybe the straight line: the sum of angles on a straight line is \( 180^\circ \). The angles are \( 41^\circ \), the right angle (\( 90^\circ \)), and \( y \). So \( 41 + 90+y=180 \), so \( y=180 - 41 - 90=49^\circ \)? Wait, no, that can't be. Wait, maybe the right - angle symbol is between the vertical line and the line forming \( x \) and \( 41^\circ \). Wait, let's look at \( x \) first. The angle \( x \) and \( 41^\circ \) are complementary because they form a right angle (since there's a right - angle symbol). So \( x + 41=90 \), so \( x = 90 - 41 = 49^\circ \). Then, for \( y \), since \( y \) is a right angle? Wait, no, the horizontal and vertical lines are perpendicular, so \( y = 90^\circ \). Wait, maybe I made a mistake. Let's re - examine.

Wait, the diagram: there is a vertical line, a horizontal line (with \( y \) on one side), a line making \( 41^\circ \) with the vertical line, and \( x \) with the horizontal line. The angle between the vertical and horizontal is \( 90^\circ \), so \( x+41 = 90 \) (since they are adjacent to the right angle), so \( x = 90 - 41=49^\circ \). And \( y \) is a right angle, so \( y = 90^\circ \)? Wait, no, the problem says "find the measure of the missing angles". Wait, maybe the right - angle symbol is between the line with \( 41^\circ \) and the horizontal line? No, the right - angle symbol is a square, so it's \( 90^\circ \). Let's correct:

Step1: Find x

The angle \( x \) and \( 41^\circ \) are complementary (they form a right angle, \( 90^\circ \)). So \( x+41 = 90 \)
\( x=90 - 41=49 \)

Step2: Find y

The angle \( y \) is a right angle (because of the right - angle symbol), so \( y = 90 \)

Answer:

\( x = 49^\circ \), \( y = 90^\circ \)