Question

warm - up: lines l and m are parallel. find the value of x in each figure. 1. figure a 2. figure b 3. figure c 4. figure d

Explanation:

Step1: Use corresponding - angles property for Figure A

Since lines $\ell$ and $m$ are parallel, the angle $x$ and the $40^{\circ}$ angle are corresponding angles. So $x = 40^{\circ}$.

Step2: Use alternate - interior angles property for Figure B

Lines $\ell$ and $m$ are parallel. The angle $x$ and the $61^{\circ}$ angle are alternate - interior angles. So $x=61^{\circ}$.

Step3: Use same - side interior angles property for Figure C

Lines $\ell$ and $m$ are parallel. The angle $x$ and the $98^{\circ}$ angle are same - side interior angles. Since same - side interior angles are supplementary ($x + 98^{\circ}=180^{\circ}$), then $x=180^{\circ}-98^{\circ}=82^{\circ}$.

Step4: Use corresponding and supplementary angles for Figure D

First, find the angle adjacent to the $125^{\circ}$ angle on line $\ell$. It is $180 - 125=55^{\circ}$ (linear - pair of angles). Then, since lines $\ell$ and $m$ are parallel, the angle $x$ and the $55^{\circ}$ angle are corresponding angles. So $x = 55^{\circ}$.

Answer:

1. $x = 40^{\circ}$
2. $x = 61^{\circ}$
3. $x = 82^{\circ}$
4. $x = 55^{\circ}$