Answer:
Angle A = 104 degrees
Angle B = 45 degrees
Angle C = 31 degrees
Step by step:
To determine the value of each angle, we need to set up an equation and solve for the variables.
Let's label the angles as A, B, and C. According to the given answer, we have:
Angle A = 4x + 34.8
Angle B = 2x + 10.4
Angle C = 2x - 3.6
To find the value of x, we need to set up an equation using the fact that the sum of the angles in a triangle is always 180 degrees.
Angle A + Angle B + Angle C = 180
Substituting the given expressions for each angle:
(4x + 34.8) + (2x + 10.4) + (2x - 3.6) = 180
Simplifying the equation:
8x + 41.6 = 180
Next, we can solve for x by isolating the variable:
8x = 180 - 41.6
8x = 138.4
x = 138.4/8
x = 17.3
Now that we have found the value of x, we can substitute it back into the expressions for each angle to determine their values:
Angle A = 4(17.3) + 34.8
Angle B = 2(17.3) + 10.4
Angle C = 2(17.3) - 3.6
Calculating the values:
Angle A = 69.2 + 34.8 = 104 degrees
Angle B = 34.6 + 10.4 = 45 degrees
Angle C = 34.6 - 3.6 = 31 degrees
Therefore, the values of each angle are:
Angle A = 104 degrees
Angle B = 45 degrees
Angle C = 31 degrees