Question

If ΔRST is an equilateral triangle, find x and y.

Answer 1

• x = 120
• y = 30

Explanation:

The value of x can be arrived at a couple of ways:

1. it is supplementary to angle RST, which is 60° in an equilateral triangle.
2. it is the sum of opposite interior angles STR and SRT, both of which are 60° in an equilateral triangle.

x° = 120°

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Triangle RSU is isosceles, so angles SUR and SRU are congruent. Their sum is 60° (which you know two ways*), so each is 30°.

y° = 30°

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* The two ways you know are based on (a) the sum of angles in a triangle is 180°, so y° +y° +120° = 180° ⇒ y = (180 -120)/2 = 30; and (b) angle RST is 60° and is the exterior angle that is the sum of opposite interior angles y° and y° ⇒ y = 60/2 = 30.