Missing angle of a Quadrilateral

How to find the missing angle of a quadrilateral?

The sum of all four angles of the quadrilateral is 360°. To find the fourth angle or the missing angle in a quadrilateral when the measurements of three angles of a quadrilateral are known, then subtract the three angles from 360° to calculate the missing angle.

Solved examples to calculate the missing angle of a quadrilateral:

1. Three angles of a quadrilateral are 54°, 80° and 116°. Find the measure of the fourth angle.

Solution:

Let the measure of the fourth angle be x°.

We know that the sum of the angles of a quadrilateral is 360°.

Therefore, 54 + 80 + 116 + x = 360

⇒ 250 + x = 360

⇒ x = (360 - 250) = 110.

Hence, the measure of the fourth angle is 110°.


2. The three angles of the quadrilateral are 90°, 105°, 85°. Find the measure of the fourth angle of a quadrilateral.

Solution:

We know that sum of all the angles of a quadrilateral is 360°.

Let the unknown angle of the quadrilateral be x.

Then 90° + 105° + 85° + x = 360°

⇒ 280° + x = 360°  

⇒ x = 360 - 280

⇒ x = 80°

Therefore, the measure of the fourth angle of the quadrilateral is 80°


3. The measures of two angles of a quadrilateral are 115°and 45°, and the other two angles are equal. Find the measure of each of the equal angles.

Solution:

Let the measure of each of the equal angles be x°.

We know that the sum of all the angles of a quadrilateral is 360°.

Therefore, 115 + 45 + x + x = 360

⇒ 160 + 2x = 360

⇒ 2x = (360 - 160) = 200

⇒ x = 100.

Hence, the measure of each of the equal angles is 100°.


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