Question

Find the values of angles x, y,and z.

51°
60°
389
Ox=91°; y = 51°; z = 31°
x=89°; y = 91°; z=0°
x= 60°; y = 120°; z = 31°
x = 91°; y = 89°; z = 31°

Answer 1

∠x = 91°

∠y = 89°

∠z = 31°

Explanation:

• the sum of the interior angles of a triangle is 180°
• the measure of third angle = the sum of the interior angles - the sum of two angles

x = 180 - (51 + 38) = 91

∠x = 91°

• the measure of ∠x and ∠y are on the straight line and they are both equal 180°

then to find the value of y = 180 - x

y = 180 - 91 = 89

∠y = 89°

z = 180 - (60 + 89) = 31

∠z = 31°

Answer 2

The value of x, y and z are:

`x=91^(0), y = 89^(0), z=31^(0)`

Explanation:

Label the image as given below.

Consider the triangle ABC.

Use the property: Sum of angles of a triangle is
`180^(0)`, to determine the value of x as follows:

`51^(0) +38^(0)+x =180^(0)\\x=91^(0)`

Use the property: Sum of angles on a straight line is
`180^(0)`, to determine the value of y as follows:

`x+y=180^(0)\\91^(0) + y = 180^(0)\\y=89^(0)`

Consider the triangle ADC.

Use the property: Sum of angles of a triangle is
`180^(0)`, to determine the value of z as follows:

`60^(0) + 89^(0) + z = 180^(0)\\z = 31^(0)`