Answer :
Answer:
• l =110°
,• o= 70°
,• s = 157°
,• p = 23°
Explanation:
Angle l
Angles l and 110° form an X-shape. Thus, they are vertical angles.
The measures of vertical angles are equal, therefore:
[tex]l=110\degree[/tex]The measure of angle l is 110 degrees.
Angle o
Angles l and o are on the same interior side of a transversal line, thus, l and o are same-side interior angles.
Same-side interior angles are supplementary, i.e. they add up to 180 degrees.
[tex]\begin{gathered} l+o=180\degree \\ 110\degree+o=180\degree \\ o=180\degree-110\degree \\ o=70\degree \end{gathered}[/tex]The measure of angle o is 70 degrees.
Angle s
Angles s and 23° are on a straight line.
The sum of angles on a straight line is 180 degrees. Therefore:
[tex]\begin{gathered} s+23\degree=180\degree \\ \text{ Subtract 23 from both sides} \\ s+23\degree-23\degree=180\operatorname{\degree}-23\degree \\ s=157\operatorname{\degree} \end{gathered}[/tex]The measure of angle s is 157 degrees.
Angle p
Angles p and 23 form a Z-shape. Thus, they are alternate angles.
The measures of alternate angles are equal, therefore:
[tex]p=23\degree[/tex]The measure of angle p is 23 degrees.