Question

What is the value of the missing angle?

Answer 1

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. =)