Question

The angle measures are represented by algebraic expressions.

Determine the values of x. y. and z.

Answer 1

The value of x is 0.5

The value of y is 0.8

The value of z is 0.9

Explanation:

* Lets explain how to find the values of x , y and z

- From the attached figure

#
`l_(1)` and
`l_(2)` intersect each other at a point

- When two lines intersect each other at a point they formed

congruent vertical opposite angles

∴ The angle of measure (50z + 13)° = the angle of measure (80z - 14)°

because thy are vertical opposite angles

∴ 50z + 13 = 80z - 14

- Add 14 to both sides

∴ 50z + 27 = 80z

- Subtract 50z from both sides

∴ 27 = 30z

- Divide both sides by 30

∴
`z=(27)/(30)=(9)/(10)=0.9`

* The value of z is 0.9

- From the attached figure

# The angles of measures (50z + 13)° and (45x + 19/2)° have sum

of 90°

∴ 50z + 13 + 45x + 19/2 = 90

∵ z = 0.9

∴ 50(0.9) + 13 + 45x + 19/2 = 90

∴ 45 + 13 + 45x + 9.5 = 90

- Add like term in the left hand side

∴ 67.5 + 45x = 90

- Subtract 67.5 from both sides

∴ 45x = 22.5

- Divide both sides by 45

∴ x = 0.5

* The value of x is 0.5

- From the attached figure

# There is a ray perpendicular to line
`l_(1)`

∴ The measure of the angle whose measure (225y/2)° is 90°

∴
`(225y)/(2)=90`

- Multiply both sides by 2

∴ 225y = 180

- Divide both sides by 225

∴
`y=(180)/(225)=(4)/(5)=0.8`

* The value of y is 0.8