Question

What are the values of x and y. In the given figure?

Answer 1

Answer:

y = 52 degrees

x = 7 degrees

Step-by-step explanation:

Hello! So, we can first easily find out the measurement of y because of the Base Angles Theorem.

[ The base angles theorem converse states if two angles in a triangle are congruent, then the sides opposite those angles are also congruent. The Isosceles Triangle Theorem states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. ]

- www.ck12.org

So basically, in an iscoceles triangle, the base angles are equal so therefore, y = 52 degrees

Now we have to solve for x. We know that the sum of the angles in a triangle are 180 so we have to make an equation:

52 + y = 14x + 6 {We know that y is 52 degrees so we should plug that in}

52 + 52 = 14x + 6 --> Now we should simplify:

104 = 14x + 6

98 = 14x

x = 7 degrees

Answer 2

Answer:

y= 52, x = 5

Step-by-step explanation:

since A = 52 degrees its the same on the otherside

so y= 52

to work out x:

(14x + 6) + 52 + 52 = 180 (sum of all angles in a triangle)

(14x + 6 ) + 104 = 180

14x +6 = 76

14x = 70

x = 5