Question

Find x and y in the diagram. A) x = 60, y = 30 B) x = 45, y = 60 C) x = 30, y = 60 D) x = 60, y = 120

Answer 1

Its choice A) x=60, y=30

Explanation:

There is a theorem that says a hypotenuse triangle and an isosceles right triangle are the two type of triangles with a 90° angle. But this triangle is a hypotenuse triangle because the other two angles aren't equivalent. Hypotenuse triangles come along with the 30 60 90 theorem. Meaning that there is one 90° angle, one 30° and one 60° angle. And its easy to tell them apart by looking at their size.

Answer 2

Answer: choice A) x = 60, y = 30

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Focus on the smaller triangle on the left side. This is an equilateral triangle with all angles the same measure. So we have three angles each x degrees. They add to x+x+x = 3x. Set this equal to 180 (all angles of any triangle add to 180) and solve

3x = 180

x = 180/3

x = 60

Since all three angles of that triangle are each 60 degrees, this means that the base angle of the smaller triangle on the left is y = 90 - x = 90 - 60 = 30.

Put another way, x+y = 60+30 = 90 because the angles x and y form the 90 degree right angle. See the attached image for more info.

note: the triangle on the right side is an isosceles triangle. The base angles are congruent, and these angles are opposite the congruent sides (marked with the tickmarks).