Question

Triangle mno is equilateral. find x and y.

Answer 1

First

Measure of any angle in an equilateral triangle is 60°

So

• 2x+4x+2x=60°
• 8x=60
• 2x=15
• x=15/2
• x=7.5

And

• 4x=4(7.5)=30

Apply angle sum property

• 2y+30=180
• 2y=150
• y=75

Answer 2

• x = 7.5 and y = 75

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Given

• Equilateral triangle MNO.

We know each interior angle of an equilateral triangle is 60°, since each of three angles are of same value.

• 180°/3 = 60°

We can see:

• m∠MNO = 2x + 4x + 2x Sum of interior angles

• 60 = 8x Substitute the value of ∠MNO
• x = 60/8 Solve for x
• x = 7.5

The middle triangle with two interior angles 4x and y has the missing angle also y, since it is isosceles, because both adjacent angles are equal at vertex N.

It gives us:

• 4x + y + y = 180 Sum of interior angles

• 4*7.5 + 2y = 180 Substitute the value of x
• 30 + 2y = 180 Solve for y
• 2y = 150
• y = 75