Virginia SOL Math / Geometry / Triangles

G.TR.1

Angles & Sides in Triangles

What you'll learn

  • Apply the Triangle Sum Theorem to find a missing angle
  • Use the Exterior Angle Theorem
  • Order the sides and angles of a triangle by size

Words to know

Triangle Sum Theorem —
the interior angles of a triangle add to 180 degrees
Exterior angle —
the angle formed by one side and an extension of another
Interior angle —
an angle inside the triangle
Isosceles triangle —
a triangle with two equal sides and two equal base angles

Why it matters Knowing that a triangle's angles always total 180 degrees lets us find missing measures in trusses, ramps, and navigation without measuring them directly.

Worked examples

Model ItI do

Two angles of a triangle measure 50 degrees and 60 degrees. Find the third angle x.

The three interior angles add to 180 degrees: 50 + 60 + x = 180. So 110 + x = 180, which gives x = 70 degrees.

Try It TogetherWe do

An exterior angle of a triangle measures 120 degrees, and one remote interior angle is 45 degrees. Find the other remote interior angle.

The exterior angle equals the sum of the two remote interior angles: 120 = 45 + y. So y = 120 - 45 = 75 degrees.

Now YouYou do

In a triangle, the sides opposite three angles measure 5, 8, and 6. Which angle is largest?

The largest angle is opposite the longest side. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Two angles of a triangle measure 40 and 75 degrees. Find the third angle.

  2. 2.Each angle of an equilateral triangle measures how many degrees?

  3. 3.In a triangle, which angle is opposite the longest side?

On Level

The core Quick Check from the book.

  1. 1.Two angles of a triangle are 90 and 35 degrees. Find the third.

  2. 2.The angles of a triangle are x, 2x, and 3x. Find x.

  3. 3.An exterior angle equals the sum of the two _____ interior angles.

  4. 4.In a triangle, which angle is opposite the shortest side: largest or smallest?

  5. 5.Each angle of an equilateral triangle measures how many degrees?

Challenge

Stretch your thinking.

  1. 1.The angles of a triangle are in the ratio 2 : 3 : 4. Find the largest angle.

  2. 2.An exterior angle of a triangle measures 130 degrees. One remote interior angle is 55 degrees. Find the other remote interior angle.

  3. 3.An isosceles triangle has a vertex angle of 40 degrees. Find one base angle.