Use the figure to find the measures of the numbered angles,
21 =
7,225,23,24= 0,25 = 0,6 = 9,27=
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Answers
Given:
A figure in which a transversal line t intersect the two parallel lines a and b.
To find:
The measure of the numbered angles.
Solution:
If a transversal line intersect the two parallel lines, then
1. Corresponding angles are equal.
2. Alternate interior angles are equal.
3. Alternate exterior angles are equal.
Now,
[tex]m\angle 1+99^\circ=180^\circ[/tex] (Linear pair)
[tex]m\angle 1=180^\circ-99^\circ[/tex]
[tex]m\angle 1=81^\circ[/tex]
[tex]m\angle 2=99^\circ[/tex] (Vertically opposite angles)
[tex]m\angle 3=\angle 1=81^\circ[/tex] (Vertically opposite angles)
[tex]m\angle 4=99^\circ[/tex] (Corresponding angles)
[tex]m\angle 5=\angle 3=81^\circ[/tex] (Alternate interior angles)
[tex]m\angle 6=99^\circ[/tex] (Alternate exterior angles)
[tex]m\angle 7=\angle 3=81^\circ[/tex] (Corresponding angles)
Therefore, [tex]\angle 1=81^\circ, \angle 2=99^\circ,\angle 3=81^\circ, \angle 4=99^\circ,\angle 5=81^\circ, \angle 6=99^\circ,\angle 7=81^\circ[/tex].
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[tex]\pink{\bigstar}[/tex] [tex]\large\leadsto\boxed{\tt\purple{x = -3}}[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
• Given:-[tex]\sf 2x - 6 = 5x + 3[/tex]⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀• Solution:-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ [tex]\sf 2x - 6 = 5x + 3[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ [tex]\sf 2x - 5x - 6 = 3[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ [tex]\sf - 3x = 3 + 6[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ [tex]\sf - 3x = 9[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ [tex]\sf x = \dfrac{9}{-3}[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
★ [tex]\large{\bold\red{x = -3}}[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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[tex]2x - 6 = 5x + 3 \\ x \: terms \: togather \\ 2x - 5x = 3 + 6 \\ - 3x = 9 \\ - x = \frac{9}{3} \\ - x = 3 \\ x = - 3 \\ thank \: you[/tex]
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