Angles BAC and Angle CAD are supplementary angles. Find the measures of each angle if the measure of Angle BAC is 10x + 16 and the measure of Angle CAD is 7x + 8. Round angle measures to the nearest tenth
To find the measures of angles BAC and CAD, we need to set up an equation based on the fact that they are supplementary angles.
Supplementary angles add up to 180 degrees, so we can write the equation:
Angle BAC + Angle CAD = 180
Substituting the given measures of the angles:
10x + 16 + 7x + 8 = 180
Combining like terms:
17x + 24 = 180
Next, we can solve for x by subtracting 24 from both sides:
17x = 180 - 24
17x = 156
Dividing both sides by 17:
x = 156 / 17
Now we can find the measure of each angle by substituting the value of x back into the expressions for Angle BAC and Angle CAD:
Angle BAC = 10x + 16
Angle CAD = 7x + 8
Angle BAC = 10(156/17) + 16
Angle CAD = 7(156/17) + 8
Calculating these expressions, we get:
Angle BAC ≈ 91.8 degrees
Angle CAD ≈ 59.5 degrees
Therefore, the measures of angles BAC and CAD are approximately 91.8 degrees and 59.5 degrees, respectively (rounded to the nearest tenth).
As you know, Bob, supplementary means they add to 180°
10x+16 + 7x+8 = 180
17x + 24 = 180
17x = 156
x = 9.176
BAC = 10*9.176+16 = 107.8
CAD = 7*9.176+8 = 72.2