ANSWERS:
For Number One.
[tex]\huge{\boxed{\large\begin{array}{l}\angle 1+51°=180° \\ \angle 1 = 180 \degree - 51 \degree \\ \angle 1 = 129 \degree \\ \overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \angle 2+64°=180° \\ \angle 2 = 180 \degree - 64 \degree \\ \angle2 = 116 \degree \end{array}}}[/tex]
For Number Two.
[tex]\huge{\boxed{\large\begin{array}{l}\angle 1+75°=180° \\ \angle 1 = 180 \degree - 75 \degree \\ \angle 1 = 105 \degree \\ \overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \angle 2+105°=180° \\ \angle 2 = 180 \degree - 105 \degree \\ \angle2 = 75 \degree \end{array}}}[/tex]
For Number Three.
• Assuming that the given hexagon is regular, thus, the measure of each interior angle is 120 degrees.
[tex]\huge{\boxed{\large\begin{array}{l}\angle 1+ \angle 2=180° \\ 120 \degree + \angle 2 = 180 \degree \\ \angle 2 = 180 \degree - 120 \degree \\ \angle 2= 60 \degree \end{array}}}[/tex]
For Number Four.
[tex]\huge{\boxed{\large\begin{array}{l}\angle 1+121°=180° \\ \angle 1 = 180 \degree - 121 \degree \\ \angle 1 = 59 \degree \\ \overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \angle 2+59°=180° \\ \angle 2 = 180 \degree - 59 \degree \\ \angle2 = 121 \degree \end{array}}}[/tex]
For Number Five.
[tex]\huge{\boxed{\large\begin{array}{l}\angle 1+37°=180° \\ \angle 1 = 180 \degree - 37 \degree \\ \angle 1 = 143 \degree \\ \overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \angle 2+102°=180° \\ \angle 2 = 180 \degree - 102 \degree \\ \angle2 = 78 \degree \end{array}}}[/tex]
REMEMBER:
• An exterior angle on a polygon is formed when you extend one of the sides of the polygon outside of the polygon.
• Hence, creating an angle that is supplementary to the interior angle at that vertex.
• As you can see, linear pairs are formed between the two adjacent angles, interior and exterior, thus, they definitely supplements each other.
