University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2019
Views:

50

Pages:

2
Author:

larbiwxcvbn

Honors Geometry Adjacent Angles: Two angles in the same plane with a common vertex and a common side, but no common interior points. Linear 1 Pair: A pair of adjacent angles whose noncommon sides are opposite rays. 2 linear pair of angles Example 1: Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. a. ∠AEB and ∠BED A + L.P. b. ∠AEB and ∠BEC A c. ∠DEC and ∠AEB not A angles A, B, C, D, and E Complementary Angles: Two angles whose measures have a sum of 90 degrees. How can the complement of an angle be found? Sub. from 90 Example 2: Use the figure at the right... a. Find the complement of ∠F. 90 - 116.5 = 26.5 angle F with a measure of 116.5 degrees b. Find the complement of ∠E. 90 - (7x - 12) = (102 - 7x) Supplementary Angles: Two angles whose measures have a sum of 180 degrees. How can the supplement of an angle be found? Sub. from 180 Example 3: Using the same figure... a. Find the supplement of ∠F. 180 - 116.5 = 63.5 b. Find the supplement of ∠E. 180 - (7x - 12) = 180 - 7x + 12 = 192 - 7x Using Complements and Supplements to Solve Problems Example 4: An angle measures 3 degrees less than twice the measure of its complement. Find the measure of the complement. Angle = x Comp. of angle1 = 90-x 1. userfiles-secure.educatorpages.com userfiles-secure.educatorpages.com x = 2(90-x) - 3 x = 180 - 2x - 3 3x = 177 x = 59 Comp. of angle = 90-59 = 31 Example 5: An angle's measure is 12 degrees more than 1/2 the measure of its supplement. Find the measure of the angle. Angle = x Supp. of angle = 180-x x = 1/2(180-x) + 12 x = 90 - 1/2x + 12 3/2x = 102 x = 68 Example 6: Light passing through a fiber optic cable reflects off the walls of the cable in such a way that angle 1 is congruent to angle 2, angle 2 and angle 3 are complementary, and angle 2 and angle 4 are complementary. If m angle 1 = 47 degrees, find m angle 2, m angle 3, and m angle 4. m angle 1 + m angle 3 = 90 degrees 47 degrees + m angle 3 = 90 degrees m angle 3 = 43 degrees m angle 2 + m angle 4 = 90 degrees 47 degrees + m angle 4 = 90 degrees m angle 4 = 43 degrees Vertical Angles: Two nonadjacent angles formed by two intersecting lines. angle 2 + angle 4 angle 1 + angle 3 Example 7: Name the pairs of vertical angles. angle HMJ and angle LMK angle HML and angle JMK