Question

1. Four of the interior angels of a hexagon measure 92, 100, 94, and 140 degrees the remaining two angles each measure (x-32) degrees. what is the value of x
2. Given right triangle abc with right angle b and cos(3x+30) = sin (12x) If angle A is (3x+10) what is the value of angle A

Answer 1

Use these steps to answer your questions.
1. Steps:
Add the terms 2x + 3x + 3x + 4x
Equate the sum of the terms to 360
Solve for x
Determine the angle measures in degrees.
Solve
2x + 3x + 3x + 4x = 360
12x = 360
x = 360/12
x = 30

Even though we know x = 30 we aren't done yet. We multiply 30 times 4 to find the biggest angle. Since 30 times 4 = 120, the biggest angle is 120 degrees. Likewise, the other angles are 3*30=90, 3*30=90, and 2*30 = 60.

2. cosB increases because ∠A and ∠B are complementary and sinA = cosB.

Hope this helps! :)

Answer 2

the sum of the interior angles of an n-sided polygon is 180(n-2)
So, the angles of a hexagon add up to 4*180 = 720, not 360.

A+B=90
sinB = cos(90-B)
cosA = cos(90-12x)
3x+30 = 90-12x
x = 4
A = 12+30 = 42°
sure enough, B = 12x = 48 = 90-42