We are given the following diagram and asked to find the value of each variable.
First we can find the value of x. To do this we will use the second part of the Inscribed Right Triangle Theorem, which states the following.
Inscribed Right Triangle Theorem
If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.
From the diagram, we can see that KM passes through the center of the circle, so it is a diameter of the circle. By this theorem angle ∠ L opposite to KM is a right angle. This allows us to conclude that x equals 90.
x=90
Now, we can find the value of y. Let's recall that by the Triangle Sum Theorem the sum of the measures of the interior angles of a triangle is 180^(∘). Therefore, the following is true.
x^(∘)+y^(∘)+40^(∘)=180^(∘)
Let's substitute x with 90 and solve this equation for y.
