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

Answer:

The value of x, y and z are:

$x=91^{0}, y = 89^{0}, z=31^{0}$

Step-by-step 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:

$60^{0} + 89^{0} + z = 180^{0}\\z = 31^{0}$

Answer 2

Answer:

∠x = 91°

∠y = 89°

∠z = 31°

Step-by-step 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°