Angles: learn and practice

Who this lesson is for

This angles lesson is for grades 5–6. Students find the missing angle in a triangle when the other two angles are known. The practice link opens that skill at grade 5. The page has one address, and both grade hubs link here. It does not measure angles with a protractor.

Three angles make a half turn

The angles inside a triangle add to 180°. A half turn, a straight line, is also 180°. You can tear the three corners off a paper triangle and set them along a straight edge. They fill the edge with no gap and no overlap. That is why knowing two angles determines the third. There is no second number that could fit.

Subtract what you already have

If two angles are known, add them and subtract the sum from 180°. The order of the two known angles does not matter. A result of 0° or a result above 180° means the given angles cannot sit together in a triangle. Angles in this lesson are measured in degrees, and the degree sign belongs on the answer.

Worked example 1: 50° and 60°

A triangle has angles 50° and 60°. Add the known angles: 50 + 60 = 110. Subtract from 180: 180 − 110 = 70. The missing angle is 70°. Check by adding all three: 50 + 60 + 70 = 180. If you had subtracted only one of the known angles, 180 − 50 = 130, the three angles would add to 240, which is too much for a triangle.

Worked example 2: a right angle and 45°

A triangle has a right angle, 90°, and another angle of 45°. The known sum is 90 + 45 = 135. The missing angle is 180 − 135 = 45°. The two smaller angles match, so the sides opposite them match as well, but this page only asks for the angle. Check: 90 + 45 + 45 = 180. A right angle uses up half of the 180° already.

Worked example 3: three equal angles

An equilateral triangle has three equal angles. Each one is 180 ÷ 3 = 60. If a problem tells you two angles are 60° and asks for the third, the same arithmetic as example 1 gives 180 − 120 = 60. All three readings agree. A triangle cannot have three right angles, because 90 + 90 + 90 = 270, which is more than 180.

Checks before you leave the problem

Add the two known angles first, then subtract that sum from 180. Add all three angles at the end and expect 180 exactly. Then practice the missing-angle skill on the board.

Common questions about angles

Do the angles of every triangle add to 180°?

Yes, for the triangles in this lesson, the ones drawn on a flat page. The three inside angles use up a half turn and no more.

What if I know only one angle?

One angle is not enough. Many different triangles can share a single angle. This page starts from two known angles.

Should the answer include the degree sign?

Yes when you are naming an angle. 70 and 70° name the same measure here. The catalog accepts both, and the degree sign makes the unit visible.