Triangle Angle-Sum & Exterior Angle Theorem
Geometry - Unit 4, Day 2
Today's Objective
Do Now: Solve for x
Find the value of x in each equation.
1. \( x + 50 + 70 = 180 \)
x =
2. \( 40 + 80 = x \)
x =
Triangle Angle-Sum Theorem
The sum of the measures of the interior angles of any triangle is always 180°.
How to Find a Missing Angle
Step 1: Identify the two angles you are given.
Step 2: Add their measures together.
Step 3: Subtract that sum from 180 to find the third angle.
Practice: Finding the Third Angle
I Do
Angles: 62°, 75°, x
\( 62 + 75 = 137 \)
\( 180 - 137 = 43 \)
\( x = 43^\circ \)
We Do
Angles: 90°, 38°, x
\( 90 + 38 = 128 \)
\( 180 - 128 = 52 \)
\( x = 52^\circ \)
You Do
Angles: \(x, 2x, 3x\)
\( x + 2x + 3x = 180 \)
\( 6x = 180 \)
\( x = 30^\circ \)
I Do: Angles: 62°, 75°, x. Find x. \(43^\circ\)
We Do: Angles: 90°, 38°, x. Find x.
You Do: Angles: \(x, 2x, 3x\). Find x.
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
How to Use the Exterior Angle Theorem
Step 1: Identify the exterior angle.
Step 2: Identify the two "remote" interior angles (the ones that are NOT adjacent to the exterior angle).
Step 3: Set up the equation:
(Remote Angle 1) + (Remote Angle 2) = (Exterior Angle)
Step 4: Solve for the missing value.
Practice: Finding Exterior Angles
I Do
Remote Interior: 50°, 70°
Exterior: x
\( 50 + 70 = x \)
\( x = 120^\circ \)
We Do
Remote Interior: 45°, x
Exterior: 110°
\( 45 + x = 110 \)
\( x = 110 - 45 \)
\( x = 65^\circ \)
You Do
Remote Interior: \(x, 2x\)
Exterior: 150°
\( x + 2x = 150 \)
\( 3x = 150 \)
\( x = 50^\circ \)
I Do: Remote Interior: 50°, 70°. Exterior: x. Find x. \(120^\circ\)
We Do: Remote Interior: 45°, x. Exterior: 110°. Find x.
You Do: Remote Interior: \(x, 2x\). Exterior: 150°. Find x.
Independent Practice
Level 1 Problems:
1. The angles in a triangle are 25°, 105°, and x. Find x.
2. The remote interior angles of a triangle are 30° and 80°. What is the measure of the exterior angle?
Level 2 Problem:
3. In \( \triangle ABC \), \( m\angle A = (x+10)^\circ \), \( m\angle B = (2x)^\circ \), and \( m\angle C = (3x-10)^\circ \). Find the measure of each angle.
Level 3 Problem:
4. An exterior angle of a triangle is 130°. One remote interior angle is four times the other. Find the measure of the two remote interior angles.
Independent Practice
1. The angles in a triangle are 25°, 105°, and x. Find x.
2. The remote interior angles of a triangle are 30° and 80°. What is the measure of the exterior angle?
3. In \( \triangle ABC \), \( m\angle A = (x+10)^\circ \), \( m\angle B = (2x)^\circ \), and \( m\angle C = (3x-10)^\circ \). Find the measure of each angle.
4. An exterior angle of a triangle is 130°. One remote interior angle is four times the other. Find the measure of the two remote interior angles.
Exit Ticket
In a triangle, two of the angles measure 54° and 82°. What is the measure of the third angle?
\( 54 + 82 = 136 \)
\( 180 - 136 = 44 \)
The third angle is 44°.