Question

Find the value of xx, y, and z in the parallelogram below

Answer 1

In a parallelogram the opposite angles are equal in measure, then, in our case:

`6y+5=71`

Solving for y:

`y=(71-5)/(6)`
`y=(66)/(6)`
`y=11`

Also, we have to consider that any two adjacent angles add up to 180°, meaning:

`(3x-8)+71=180`
`3x-8+71=180`
`3x+63=180`
`x=(180-63)/(3)`
`x=(117)/(3)`
`x=39`

Using the same logic as the one used to calculate y, we can do the following:

`(6z+7)=(3x-8)`

However, as we know x = 39° we can solve for z:

`6z+7=3\cdot(39)-8`
`6z=117-8-7`
`z=(102)/(6)`
`z=17`

Answer:

• x = 39°

,

• y = 11°

,

• z = 17°