1 / 4

XYZW is an isosceles trapezoid, and m  X = 156. Find m  Y , m  Z , and m  W .

m  X + m  W = 180. Two angles that share a leg of a trapezoid are supplementary. 156 + m  W = 180. Substitute. m  W = 24. Subtract 156 from each side. Trapezoids and Kites. LESSON 6-5. Additional Examples.

frisco
Download Presentation

XYZW is an isosceles trapezoid, and m  X = 156. Find m  Y , m  Z , and m  W .

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. mX + mW = 180 Two angles that share a leg of a trapezoid are supplementary. 156 + mW = 180 Substitute. mW = 24 Subtract 156 from each side. Trapezoids and Kites LESSON 6-5 Additional Examples XYZW is an isosceles trapezoid, and mX = 156. Find mY, mZ, and mW. Because the base angles of an isosceles trapezoid are congruent, mY = mX = 156 and mZ = mW = 24. Quick Check

  2. Trapezoid ABDC is part of an isosceles triangle whose vertex angle is at the center of the spider web. Because there are 6 adjacent congruent vertex angles at the center of the web, together forming a straight angle, each vertex angle measures , or 30. 180 6 Trapezoids and Kites LESSON 6-5 Additional Examples Half of a spider’s web is shown below, formed by layers of congruent isosceles trapezoids. Find the measures of the angles in ABDC. By the Triangle Angle-Sum Theorem, mA + mB + 30 = 180, so mA + mB = 150. Because ABDC is part of an isosceles triangle, mA = mB, so 2mA = 150 and mA = mB = 75.

  3. Another way to find the measure of each acute angle is to divide the difference of 180 and the measure of the vertex angle by 2: 180 – 30 2 = 75 Because the bases of a trapezoid are parallel, the two angles that share a leg are supplementary, so m C = m D = 180 – 75 = 105. Trapezoids and Kites LESSON 6-5 Additional Examples (continued) Quick Check

  4. Diagonals of a kite are perpendicular. m 2 = 90 RU = RS Definition of a kite m 1 = 72 Isosceles Triangle Theorem m 3 + mRDU + 72 = 180 Triangle Angle–Sum Theorem m RDU = 90 Diagonals of a kite are perpendicular. m 3 + 90 + 72 = 180 Substitute. m 3 + 162 = 180 Simplify. m 3 = 18 Subtract 162 from each side. Trapezoids and Kites LESSON 6-5 Additional Examples Find m 1, m 2, and m 3 in the kite. Quick Check

More Related