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Features

Sort angles as acute, right, obtuse and straight, and measure them with a protractor
See the three corners of a triangle line up into a straight angle
Measure the angles of triangles drawn at true size and add them: always 180°
Find an unknown angle of a triangle with the equation 180 − a − b
Read tick marks, arcs and right-angle squares on isosceles and right triangles
Name triangles by their angles and sides, and decide which triangles can exist
Unknown angles on a line, in a right angle and around a point, and story problems
Every page in color and in black and white
Answer keys included

Skills Covered

Sort angles as acute, right, obtuse or straight, and measure them in whole degrees
Explain why the angles of a triangle add up to 180°
Find the unknown angle of a triangle from the other two

Read the marks for equal sides, equal angles and right angles
Name triangles by their angles and by their sides, and tell which can exist
Find unknown angles on a line, in a right angle and around a point

How to Use This Pack

Five pages on angles and the angles of a triangle. Page 1 sorts angles by sight into acute, right, obtuse and straight, then measures angles with your own protractor (every angle is drawn at its true size, so it measures the same on any printer) and picks the right tool for a job. Page 2 tears the three corners off a triangle and lines them up: together they make a straight angle, 180°. Then students measure the angles of four triangles and add them, and the sum is always 180°. Page 3 finds the unknown angle of a triangle by subtracting the two angles it knows from 180 (180 − 62 − 45 = 73), right triangles included, then uses tick marks and arcs on isosceles triangles: the equal angles are marked the same way. Page 4 names triangles by their angles and by their sides from their measures and marks, and asks which triangles can exist: two right angles leave nothing for the third angle. Page 5 finds unknown angles on a straight line (180°), in a right angle (90°) and around a point (360°), then two story problems. Every page starts with a worked example.

In the Classroom

Before page 2, have every student cut out a paper triangle of any shape, tear off its three corners and fit them together at a point on a straight line. Every triangle in the room makes the same straight angle. Then compare measured sums on page 2: a sum of 179° or 181° is a measuring slip, which is a good moment to practice lining up the protractor again.

At Home

Look for triangles around the house: a slice of sandwich, a roof, a coat hanger. Ask whether each one has a right angle, an obtuse angle or only acute angles, and whether any of its sides look equal. If you have a protractor, measure two corners and predict the third before measuring it.

Tips for Success

Acute is less than 90°, right is exactly 90°, obtuse is between 90° and 180°, straight is 180°
Put the center of the protractor on the vertex and the 0 line on one side
The three angles of every triangle add up to 180°
To find the third angle, subtract the two angles you know from 180
Sides with the same tick marks are equal, and angles with the same arcs are equal

Common Core Standards Alignment

This pack supports the following Common Core State Standards for Mathematics:

4.MD.C.5a Know an angle's size is the share of a circle (centered at its vertex) between its rays; one degree is 1/360 of a full turn.
4.MD.C.5b Know that an angle made of some number of one-degree turns measures that many degrees, so 50 one-degree turns make 50°.
4.MD.C.6 Use a protractor to find the size of an angle to the nearest whole degree, and draw angles of a given size.
4.MD.C.7 Know that angle measures add up when an angle is split into parts, and find unknown angles in diagrams by adding or subtracting, using equations.
4.G.A.1 Draw and find points, lines, line segments, rays, right, acute and obtuse angles, and parallel and perpendicular lines, including in flat shapes.
4.G.A.2 Sort flat shapes by whether they have parallel or perpendicular lines or angles of a certain size, and recognize right triangles as a group.
5.G.B.3 Know that a shape in a smaller group has every feature of the larger group: squares are rhombuses, so all squares have four equal sides.
5.G.B.4 Sort flat shapes into a hierarchy by their properties, such as polygons, quadrilaterals, parallelograms, rectangles and squares.

Angles of a Triangle

5th Grade

Angles sorted and measured, and why the three angles of every triangle add up to 180°. Students sort and measure angles, tear and measure the corners of triangles, find unknown angles in triangles and diagrams, and name triangles by their angles and sides.

Download PDF

What’s Included

5 worksheets in color and in black and white, with answer keys (15 pages)
Sorting angles, measuring angles drawn at true size, and choosing a tool
The 180° sum shown with torn corners and with measured triangles
Unknown angles in triangles and diagrams, naming triangles, and story problems

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Free to print and share

This worksheet is free to download, print, copy, and hand out in your classroom or at home. You do not need to create an account, and there are no watermarks on the PDF.