Lesson 12 Lines Angles Angle Sum of a

Lesson 12 Lines & Angles Angle Sum of a Quadrilateral

Warm-Up Find the value of x.

Angle Sum of a Quadrilateral Target: Find angle measures in a quadrilateral.

Vocabulary � Quadrilateral: A polygon with four sides.

Quadrilateral Angle Sum The sum of the measures of the angles of a quadrilateral is 360°.

Example 1 Set up an equation and solve for x. � The sum of the angles of a quadrilateral is 360°. 51 + 110 + 33 + x = 360 � Combine like terms. 194 + x = 360 � Subtract 194 from each side. – 194 x = 166 �✔ 110 + 51 + 33 + 166 = 360

Example 2 ab In quadrilateral QUAD, m U = 2 x°, m A = (x + 30)°, U ≅ D and Q is a right angle. a. Draw a diagram and label it. b. Set up and equation and solve for x. � 90 � � � + 2 x + (x + 30) + 2 x = 360 120 + 5 x = 360 – 120 5 x = 240 5 5 x = 48

Example 2 c In quadrilateral QUAD, m U = 2 x°, m A = (x + 30)°, U ≅ D and Q is a right angle. c. Find the degree measure for each angle. In 2 b, x = 48. To find the degree measures substitute 48 for x. � m Q = 90° � m U = m D = 2(48) = 96° � m A = ((48) + 30) = 78°

Exit Problems Set up an equation and solve for x. 1. 2. 3. Find the measure of B in #2.

Communication Prompt What is the connection between the sum of the angles in a triangle and the sum of the angles in a quadrilateral?