Question

Work out the size angles x,y and z​

Answer 1

The values of x, y, and z are
`64` degrees,
`64` degrees, and
`20` degrees respectively.

In the given figure we can see that triangle ABD is an isosceles triangle.

This means that the angles x and y will be equal to each other.

Therefore we can calculate x and y as:

`52 + x + y = 180` (using the property of the sum of all angles in a triangle)

Substitute y with x because they are equal:

`52 + x + x = 180\\52 + 2x = 180\\2x = 180 - 52\\x = 128 / 2\\x = 64`

Since x = y, thus, y is also equal to
`64`.

Now we will calculate z:
Angle ADC is making a linear pair with y.

Therefore,
`ADC + y = 180\\ADC = 180 - 64\\ADC = 116`

`ADC + z + 44 = 180` (sum of all angles in a triangle)

`116 + z + 44 = 180\\z = 180 - 116 - 44\\z = 180 - 160\\z = 20`

Answer 2

x = y = 14

z = 70

Explanation:

As we can see from the markings, x = y

So we have an isosceles triangle in ABD

the sum of angles in a triangle is 180

52 + x + y = 180

x + y = 180-52

x + y = 28

so since x = y

x = y = 14

To get z, we have that;

52 + z + 14 + 44 = 180

z + 110 = 180

z = 180-110

z = 70