Question

Find the value of x and y.

Answer 1

Answer:

x = 9

y = 36

Step-by-step explanation:

Lines and Angles

Triangle CDE is isosceles. This means the two angles of the base DE are congruent (have the same measure):

7x + 1 = 4x + 28

Subtracting 4x + 1:

3x = 27

Dividing by 3:

x = 9

Substituting in the expression for the angles:

7x + 1 = 7*9 + 1 = 64°

The angles are 64° and 64°. The other internal angle at vertex C is 180°-64°-64°=52°. This angle is congruent with its vertical angle in the triangle ABC. We are given another angle of 43°. Thus the measure of angle A is 180°-52°-43°=85°

This last angle is equal to the expression of y:

-2(3 - y) + 19 = 85

Subtracting 19:

-2(3 - y) = 66

Removing the parentheses:

-6 + 2y = 66

Adding 6:

2y = 72

Dividing by 2:

y = 36

Final answer:

x = 9

y = 36