By Dr. Wilfred Funk, Norman Lewis
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C. ∠1 is the vertical angle to ∠TLK, which is given. ∠2 is the vertical pair to ∠NOM, which is also given. Since vertical angles are congruent, ∠1 and ∠2 measure 42° and 97°, respectively. To ﬁnd the measure of ∠3, subtract the sum of ∠1 and ∠2 from 180° (the sum of the measure of a triangle’s interior angles): 180 – (42 + 97) = m∠3 41 = m∠3 99. a. There are two ways to ﬁnd the measure of exterior angle OPS. The ﬁrst method subtracts the measure of ∠3 from 180°. The second method adds the measures of ∠1 and ∠2 together because the measure of an exterior angle equals the sum of the two nonadjacent interior angles.
73. True. When two lines intersect, they create four angles. The two angles opposite each other are congruent. Adjacent angles are supplementary. If vertical angles are acute, angles adjacent to them must be obtuse in order to measure 180°. 74. False. Vertical angles cannot be equal to or more than 180°; otherwise, they could not form supplementary angle pairs with their adjacent angle. 75. False. Perpendicular lines form all right angles. 76. True. Adjacent interior angles form supplementary pairs; their joint measurement is 180°.
108. ∠SBO and ∠OCU are congruent. When two angles are supplementary to the same angle or angles that measure the same, then they are congruent. Set 22 109. Equal. Together ∠5 and ∠6 form the vertical angle pair to ∠2. Consequently, the angles are congruent and their measurements are equal. 110. A determination cannot be made. ∠1 and ∠3 may look like vertical angles, but do not be deceived. Vertical angle pairs are formed when lines intersect. The vertical angle to ∠1 is the full angle that is opposite and between lines m and l.