Angles BAC and Angle CAD are supplementary angles. Find the measures of each angle if the measure of Angle BAC is 18x + 16 and the measure of Angle CAD is 15x + 8. Round angle measures to the nearest tenth.
Two Angles are Supplementary if they add up to 180 degrees.
(18x+16) + (15x+8) = 180
Solve for x and then the angles.
To find the measures of angles BAC and CAD, we need to set up an equation based on the fact that the angles are supplementary.
Supplementary angles add up to 180 degrees. So, we can set up the equation:
Angle BAC + Angle CAD = 180 degrees
Substituting the given measures, the equation becomes:
(18x + 16) + (15x + 8) = 180
Combine like terms:
33x + 24 = 180
Next, we isolate the variable x by subtracting 24 from both sides:
33x = 180 - 24
33x = 156
Now, divide both sides by 33 to solve for x:
x = 156/33
x ≈ 4.7
Substitute x back into the expressions for Angle BAC and Angle CAD:
Angle BAC = 18x + 16
Angle BAC ≈ 18(4.7) + 16
Angle BAC ≈ 84.6 + 16
Angle BAC ≈ 100.6 degrees
Angle CAD = 15x + 8
Angle CAD ≈ 15(4.7) + 8
Angle CAD ≈ 70.5 + 8
Angle CAD ≈ 78.5 degrees
Therefore, the measure of angle BAC is approximately 100.6 degrees, and the measure of angle CAD is approximately 78.5 degrees.