# Chapter 10 - Geometry - 10.1 Points, Lines, Planes, and Angles - Exercise Set 10.1 - Page 617: 33

The measurement of angle 1 is $65{}^\circ$and angle 2 is $56{}^\circ$and angle 3 is$124{}^\circ$.

#### 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 vertical angles are equal and therefore the angle measuring 65° and angle 1 will be equal thus, the measure of angle 1 will be 65°. As it can be seen in the figure, that the angle 1, angle 2 and the angle measuring 59° forms a straight angle and the measure of a straight angle is 180°, thus, the measure of angle 2 will be as follows: \begin{align} & \measuredangle 1+\measuredangle 2+59{}^\circ =180{}^\circ \\ & 65{}^\circ +\measuredangle 2+59{}^\circ =180{}^\circ \\ & \measuredangle 2=180{}^\circ -65{}^\circ -59{}^\circ \\ & =56{}^\circ \end{align} Now, it is known that the measure of corresponding angles are equal and $\measuredangle 1+59{}^\circ$and$\measuredangle 3$ are corresponding angles, thus, a measure of $\measuredangle 3$ will be equal to $\measuredangle 1+59{}^\circ$ and therefore, a measure of $\measuredangle 3$ will be as follows: \begin{align} & \measuredangle 3=\measuredangle 1+59{}^\circ \\ & =65{}^\circ +59{}^\circ \\ & =124{}^\circ \end{align}

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