Question

Need help with this question.

Find the values of x,y, and z. The diagram is not to scale.

Answer 1

Small triangle needs to equal 180degrees.
so
180 = 63 + 36 + x
180 = 99 + x
subtract 99 from both sides to isolate x
81 = x

Now, x and z are supplementary angles.
Meaning that they add up to 180degrees

x + z = 180
81 + z = 180
subtract 81 from both sides to isolate z
z = 99

Now we can see there is a triangle formed with the top angle 13 degrees and z and y
they must all add up to 180.
180 = 13 + z + y
we know z = 99
180 = 13 + 99 + y
180 = 112 + y
68 = y

Hope this helps!

Answer 2

x = 81°, z = 99°, y = 68°

Explanation:

For a triangle, the sum of internal angles is 180°

So for the triangle in the left:

36 + 63 + x =180°

99 + x = 180

x = 180 - 99

x = 81°

For the triangle in the right:

x + z =180 since they are suplementary angles

81 + z = 180

z = 180 -81

z = 99°

an the sum of all the internal angles of the triangle in the right:

13 + 99 + y = 180

112 + y = 180

y = 180 - 112

y = 68°