The measure of the two angles are: [tex]\mathbf{85^{\circ} $ and $ 95^{\circ}}[/tex]
- The figure shows two interior angles that lie on the same side of the transversal.
- Both angles are same-side-interior angles.
- Same-side-interior angles are supplementary angles which add up to 180 degrees
[tex]20x + 5 + 24x - 1= 180[/tex]
[tex]44x + 4 = 180[/tex]
- Subtract 4 from both sides
[tex]44x = 180 - 4\\\\44x = 176[/tex]
[tex]x = 4[/tex]
- Find the measure of each angle given in the figure
[tex]20x + 5[/tex]
[tex]20(4) + 5 \\\\= 80 + 5\\\\= 85^{\circ}[/tex]
[tex]24(4) - 1 \\\\= 96 - 1\\\\= 95^{\circ}[/tex]
The measure of both angles are [tex]\mathbf{85^{\circ} $ and $ 95^{\circ}}[/tex]
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