Question

question
find the values of x and y
(image of a right triangle with a segment inside, angles marked y°, 40°, and x°, and some congruent marks)
answer attempt 1 out of 5
x =

y =

Explanation:

Step1: Find the value of \(x\)

Since the two triangles are congruent (by the Hypotenuse - Leg congruence for right - angled triangles, as the right - angle sides are equal and the hypotenuse is common), the angle \(x\) is an exterior angle of the right - angled triangle. By the exterior angle property of a triangle (an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles), \(x = 90^{\circ}+40^{\circ}\).

$$x=130^{\circ}$$

Step2: Find the value of \(y\)

In the right - angled triangle, using the angle - sum property of a triangle (\(180^{\circ}\) in a triangle). Let the other non - right angle in the right - angled triangle be \(z\). Since the two right - angled triangles are congruent, \(z = 40^{\circ}\). Then \(y+z + 90^{\circ}=180^{\circ}\), substituting \(z = 40^{\circ}\), we get \(y+40^{\circ}+90^{\circ}=180^{\circ}\), so \(y=180^{\circ}-90^{\circ}-40^{\circ}\).

$$y = 50^{\circ}$$

Answer:

\(x = 130\), \(y = 50\)