Practice Angle sums in triangles and quadrilaterals
The interior angles of a triangle add up to 180 degrees in plane geometry.
This relationship helps you calculate missing angles and check geometric constructions.
Exercises with solutions
In every triangle the interior angles add up to 180 degrees, in every quadrilateral to 360 degrees. In general, a polygon with n corners has the angle sum (n − 2) · 180 degrees. Angles next to each other on a straight line add up to 180 degrees.
Exercise 1
In a triangle two angles are 65° and 48°. How large is the third?
Show solution and working
67°
180° − (65° + 48°) = 180° − 113° = 67°.
Exercise 2
What is the angle sum in a quadrilateral?
Show solution and working
360°
(4 − 2) · 180° = 2 · 180° = 360°.
Exercise 3
What is the angle sum in a pentagon?
Show solution and working
540°
(5 − 2) · 180° = 3 · 180° = 540°.
Exercise 4
A right-angled triangle has angles of 90° and 37°. How large is the third angle?
Show solution and working
53°
180° − 90° − 37° = 53°.
Common mistake
Using the triangle angle sum for quadrilaterals too. Each extra corner adds 180 degrees. And overlooking that a triangle cannot have an angle of 0° or 180°.
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