Question

Find the value
X
of X and Y.

Answer 1

X=60° Y=30°

Explanation:

I recreated your figure in the correct scale and then just measured with a protractor.

X:

If all the lines with the little line on them are equal to each other, then the triangle with the x in it is an equilateral triangle. This means that each angle in that one are 60° because according to the triangle angle sum theorem, all three interior angles of a triangle must add up to 180°. So if you divide that by 3 because this is an equilateral triangle, you get 60°.

Y:

Because the angle to the right of X is also 60°, and the two lines that connect across X and Y create a 180° flat line, they are supplementary and we can subtract 60 from 180 to get the angle to the left of Y. 180-60=120

If we use the Triangle Angle Sum theorem again, we find out that the remaining two angles in the triangle on the right add up to 60. 180-120=60.

Since two of those lines are equal, the last two angles have to be equal. So 60/2=30. Therefore, ∠Y=30°

Answer 2

x = 60°

y = 120°

Explanation:

the triangle on the left is equilateral, 3 congruent sides and 3 congruent angles, (see signs on the sides) therefore the angle is 60° (the sum of the internal angles in the triangles is 180°, 180 : 3 = 60)

the triangle on the right is isosceles, two congruent sides and two congruent angles, we consider the line that goes from x to y, it is 180°, we remove the 60° of the equilateral triangle from 180° and we have 120°

x = 60°

y = 120°