Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.1 Points, Lines, Planes, and Angles - Exercise Set 10.1 - Page 617: 34


The measurement of angle 1 is \[63{}^\circ \]and angle 2 is \[57{}^\circ \]and angle 3 is\[120{}^\circ \].

Work Step by Step

The given figure shows two parallel lines that are intersected by two transversal lines. Now, using the fact that the alternate and corresponding angles are equal the measure of required angles can be found which is as follows: Now it is known that the alternate interior angles are equal and the angle measuring 63° and \[\measuredangle 1\] are alternate interior angles, therefore, the angle measuring 63° and \[\measuredangle 1\] will be equal thus, the measure of \[\measuredangle 1\] will be 63°. As it can be seen in the figure, that the \[\measuredangle \]1, \[\measuredangle \]2 and the angle measuring 60° forms a straight angle and the measure of a straight angle is 180°, thus, the measure of \[\measuredangle 2\] will be as follows: \[\begin{align} & \measuredangle 1+\measuredangle 2+60{}^\circ =180{}^\circ \\ & 63{}^\circ +\measuredangle 2+60{}^\circ =180{}^\circ \\ & \measuredangle 2=180{}^\circ -123{}^\circ \\ & =57{}^\circ \end{align}\] Thus, the measure of angle 2 is 57° Now, it is known that the measure of corresponding angles are equal and \[\measuredangle 1+\measuredangle 2\]and\[\measuredangle 3\]are corresponding angles, thus, a measure of \[\measuredangle 3\] will be equal to \[\measuredangle 1+\measuredangle 2\] and therefore, a measure of \[\measuredangle 3\] will be as follows: \[\begin{align} & \measuredangle 3=\measuredangle 1+\measuredangle 2 \\ & =63{}^\circ +57{}^\circ \\ & =120{}^\circ \end{align}\]
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