Answer:
• d=70°
,• f=110°
,• h=125°
,• g=55°
Explanation:
Angle d
Angles d and 110° are on a straight line.
The sum of angles on a straight line is 180 degrees. Therefore:
[tex]\begin{gathered} d+110\degree=180\degree \\ \text{ Subtract 110 from both sides} \\ d+110\operatorname{\degree}-110\degree=180\operatorname{\degree}-110\degree \\ d=70\operatorname{\degree} \end{gathered}[/tex]The measure of angle d is 70 degrees.
Angle f
Angles f and 110° form a Z-shape. Thus, they are alternate angles.
The measures of alternate angles are equal, therefore:
[tex]f=110\degree[/tex]The measure of angle f is 110 degrees.
Angle h
Angles h and 125° form a Z-shape. Thus, they are alternate angles.
The measures of alternate angles are equal, therefore:
[tex]h=125\degree[/tex]The measure of angle h is 125 degrees.
Angle g
Angles g and 125° are on a straight line.
The sum of angles on a straight line is 180 degrees. Therefore:
[tex]\begin{gathered} g+125\degree=180\degree \\ \text{ Subtract 125 from both sides} \\ g+125\degree-125\degree=180\operatorname{\degree}-125\degree \\ g=55\operatorname{\degree} \end{gathered}[/tex]The measure of angle g is 55 degrees.