The measures of three angles of a quadrilateral are 80, 90, and 103 degrees.

Find the measure of the fourth angle.

A.) 67°

B.) 77°

C.) 87°

D.) 97°

Question

The measures of three angles of a quadrilateral are 80, 90, and 103 degrees.

Find the measure of the fourth angle.

A.) 67°

B.) 77°

C.) 87°

D.) 97°

mathstudent55 · Answer

The formula for the sum of the angles of a polygon is:

$S = (n - 2)180$

where S = sum of the measures of the angles, and n = number of sides.

In this problem, you know you have 4 sides since you have a quadrilateral.
Use the formula with n = 4 and find the sum of the measures of the angles.
What do you get?

mathstudent55 · Answer

$S = (n - 2)180$

$S = (4 - 2)180$

What do you get for S?

anonymous · Answer

Which s?

mathstudent55 · Answer

In the formula above. S is the sum of the measures of the angles.
Just see it below:

$S = (n - 2)180$

$S = (4 - 2)180 $

What is S equal to?

mathstudent55 · Answer

First, do 4 - 2.
What is 4 - 2?

triciaal · Answer

sum of the  4 angles in a quadrilateral = 360   and you have 3

anonymous · Answer

2

mathstudent55 · Answer

Good.
Now what is 2 * 180 = ?

anonymous · Answer

360

mathstudent55 · Answer

Great

$S = (4 - 2) 180$

$S = 2(180) $

$S = 360$

The sum of the measures of the angles of a quadrilateral is 360.

mathstudent55 · Answer

We are given the measures of 3 angles.
We know the sum of all 4 angles, so we subtract the measure of each angle from 360 to find the missing measure.

mathstudent55 · Answer

What is:
360 - 80 - 90 - 103 = ?

Or you can first add 80 + 90 + 103, and then subtract this sum from 360.

anonymous · Answer

87

anonymous · Answer

Thank you so much, again!

mathstudent55 · Answer

Correct.
Good job!

mathstudent55 · Answer

You're welcome.