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mhanifa

Answer:

  • 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

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

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