Question

Triangle MNO is equilateral. Find x and y.

Answer 1

Again, your getting lost in the numbers. just think simply. a triangle has 180° and equilateral means all angles are exactly the same. Because of this, you know that m,n&o all equal 60°.

now it gets a little more complex when you split that to the smaller triangle and each of those have 180° within them.

it's safe to say that N is splitting it's full 60° equally between the three within it. making each one of the points at N equal to 20°. so solve for the rest to get y°.

We know M= 60°, O= 60°, N= 60° (20°,20°,20°) so to complete the triangle on the left we have one more angle that must be 100°. to complete the triangle on the right we have one more angle that must be 100° and to complete the center triangle we only know of 20° but have two equal angles left. So 180°-20°=160°. 160°÷2angles= 80° per angle to complete the center triangle.

that gives us y°=80°.

the X's are adding the smaller triangles to make the bigger triangle. so take 2x+4x+2x and divide that from the big triangle 180°. 8x=180° means x°=22.5°