SaiBook.us Geometry

Lesson Example Discussion Quiz: Class Homework

Example

Title: Angles

Grade: 6-a Lesson: S2-L3

Explanation: The best way to understand geometry is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

In a quadrilateral ABCD, the measures of ∠A, ∠B, and ∠C are 70º, 120º, and 50º, respectively. Find the measure of ∠D.

Step 1a

The sum of the angles in a quadrilateral is always 360º.

To find the measure of ∠D, we subtract the sum of angles ∠A, ∠B, and ∠C from 360º.

$1a$

Explanation: The sum of a quadrilateral’s angles equals 360º; ∠D = 360 - (∠A + ∠B + ∠C).

Step 1b

∠A + ∠B + ∠C + ∠D = 360º.

Now plug the values 70º + 120º∘ + 50º∘ + ∠D = 360º.

240º + ∠D = 360º.

Explanation: ∠A + ∠B + ∠C + ∠D = 360º.

Now plug in the values: 70º + 120º∘ + 50º∘ + ∠D = 360º.

240º + ∠D = 360º.

Step 1c

∠D = 360º - 240º = 120º.

Therefore, the measure of ∠D is 120º.

Explanation: To find the measure of angle D, you need to subtract its known angle of 240 degrees from 360 degrees (a full circle). This gives us 120 degrees.