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
To solve these questions, we need to use the property that the sum of all interior angles of a hexagon is equal to 720 degrees (6 * 180).
1. For the first question, we're given that four interior angles of the hexagon measure 92, 100, 94, and 140 degrees. Let's find the sum of these four angles:
Sum = 92 + 100 + 94 + 140 = 426 degrees.
Next, let's find the sum of the remaining two angles, which each measure (x-32) degrees.
(x-32) + (x-32) = 2x - 64 degrees.
Now we can set up an equation using the sum of all interior angles of the hexagon:
Sum = 426 + (2x - 64) = 720 degrees.
Simplifying the equation, we get:
2x - 64 = 720 - 426
2x - 64 = 294
Solving for x:
2x = 358
x = 179
Therefore, the value of x is 179.
2. For the second question, we're given that cos(3x+30) = sin (12x) and we need to find the value of angle A, given as (3x+10).
Using the trigonometric identity sin(A) = cos(90 - A), we can rewrite the equation:
cos(3x+30) = cos(90 - 12x)
Since the trigonometric functions are equal, the angles inside them must be equal as well. Therefore:
3x + 30 = 90 - 12x
Simplifying the equation, we get:
3x + 12x = 90 - 30
15x = 60
x = 4
Now let's substitute the value of x into angle A = (3x+10):
A = 3(4) + 10 = 12 + 10 = 22
Therefore, the value of angle A is 22 degrees.
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! :)
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