Question 1.
Formula for the sum of the measures of the interior angles of an n-sided polygon:
S = 180° · (n – 2)
A hexagon has 6 edges (hence 6 interior angles), so for this question, the that sum is
S = 180° ·(6 – 2) (n = 6)
S = 180° · 4
S = 720° <——— sum of the interior angles of a hexagon.
Then, just sum all the measures of the interior angles and it must be equal to 720°:
150° + 95° + 105° + 145° + 95° + x = 720°
590° + x = 720°
x = 720° – 590°
x = 130° <——— this is the measure of the missing angle.
The second option is the correct: 130°.
—————
Question 2.
• length of the triangle's base: b = 8.7 ft;
• length of the corresponding height: h = 4.5 ft.
The area of the triangle is given by this formula. Just plug in values:
b × h
A = ————
2
(8.7 ft) × (4.5 ft)
A = —————————
2
8.7 × 4.5
A = —————— ft²
2
39.15
A = ———— ft²
2
A = 19.575 ft² <——— this is the correct answer (second option).
I hope this helps. =)
