Question

Find the measure of the three missing angles in the parallelogram below.

Answer 1

`x` = 67 ,
`y` = 113 ,
`z` = 67

Explanation:

What we need to know:

A parallelogram has two pairs of equal angles

Opposite angles are equal

Angles in a quadrilateral add up to 360

1) Find out as many angles we can

We know that the opposite angles are equal, this means that y would be equal to 113

• y = 113

2) Find the remaining angles

We already know that two of our angles are 113, this means that our total is 226 for now. We have two angles left which are equal so to find them we have to subtract 226 by 360 then divide by 2

• 360 - 226 = 134
• 134 ÷ 2 = 67
• 
  `x` = 67
• 
  `z` = 67

Hope this helps, have a lovely day! :)

Answer 2

x = 67

y = 113

z = 67

Explanation:

The properties of a parallelogram are:

• 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 z are adjacent to the angle that measures 113°.

Since adjacent angles in a parallelogram are supplementary:

⇒ x° + 113° = 180°

⇒ x° = 67°

⇒ x = 67

Similarly:

⇒ z° + 113° = 180°

⇒ z° = 67°

⇒ z = 67

As opposite angles in a parallelogram are equal:

⇒ y° = 113°

⇒ y = 113