The angles are [tex]\boxed{{{115}^\circ }}[/tex] and [tex]\boxed{{{65}^\circ }}[/tex] if difference of the same side interior angles of two parallel lines is [tex]{50^ \circ }.[/tex]
Further Explanation:
Vertical angles can be defined as the angles that are opposite to each other if two lines cross each other.
Acute angles are those angles in which the measurement of the angle is less than [tex]{90^ \circ }.[/tex]
The sum of the angles on the same side of the transversal is [tex]{180^ \circ }.[/tex]
Given:
The difference between the two angles is [tex]{50^ \circ }.[/tex]
Explanation:
Consider the first angle be [tex]x[/tex] and consider the second angle be [tex]y[/tex].
The sum of [tex]x + y[/tex] is [tex]{180^ \circ }.[/tex]
[tex]x + y = {180^ \circ }[/tex]
The difference between [tex]x[/tex] and [tex]y[/tex] is [tex]{50^ \circ }.[/tex]
[tex]\begin{aligned}x - y&= 50\\x&= 50 + y\\\end{aligned}[/tex]
Substitute [tex]50+y[/tex] for x is equation [tex]x+y=180.[/tex]
[tex]\begin{aligned}50 + y + y&= 180\\2y &= 180- 50\\2y&= 130\\y&= \frac{{130}}{2}\\y&= 65\\\end{aligned}[/tex]
The angles are [tex]\boxed{{{115}^\circ }}[/tex] and [tex]\boxed{{{65}^\circ }}[/tex] if difference of the same side interior angles of two parallel lines is [tex]{50^ \circ }.[/tex]
Kindly refer to the image attached.
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Angles
Keywords: vertical angle, opposite angle, angles, alternate angles, linear pair, corresponding angles, analyze, value of x.
