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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