Question

What is the measure of the three missing angles in the rhombus below?

Answer 1

x = 100

y = 100

z = 80

Explanation:

The properties of a rhombus are:

• All sides are equal in length.
• The opposite sides are equal and parallel.
• Opposite angles are congruent.
• Adjacent angles are supplementary (sum to 180°).

Two angles are said to be adjacent when they share a common vertex.

Therefore, both angle x and angle y are adjacent to the angle that measures 80°.

Since adjacent angles in a rhombus are supplementary:

⇒ x° + 80° = 180°

⇒ x° = 100°

⇒ x = 100

Similarly:

⇒ y° + 80° = 180°

⇒ y° = 100°

⇒ y = 100

As opposite angles in a rhombus are equal:

⇒ z° = 80°

⇒ z = 80

Answer 2

`x` = 100 ,
`y` = 100 ,
`z` = 80

Explanation:

Information we need to know:

Opposite angles in a rhombus are equal

Angles in a quadrilateral equal to 360

1) Find any angles that we can

We already know that opposite angles are 80. This means that we can easily see that
`z` is 80.

The total we have at the moment is 160

2) Find the remaining angles

If we know that all angles in a quad add up to 360, we can easily find
`x` and
`y` by taking 160 from 360 and the dividing by 2!

• 360 - 160 = 200
• 200 ÷ 2 = 100
• 
  `x` = 100
• 
  `y` = 100

TOP TIP:

To make sure our answer is correct we can add all our answers up and check that they add up to 360

• 100 + 100 + 80 + 80 = 360

Our answer is correct!

Hope this helps, have a great day! :)