The figure shows adjacent angles BAC and CAD.
Adjacent angles BAC and CAD sharing common ray AC
Given:
m∠BAD = 134°
m∠BAC = (2x + 3)°
m∠CAD = (4x −1)°
Part A: Using the angle addition postulate, write and solve an equation for x. Show all your work. (6 points)
Part B: Find the m∠CAD. Show all your work. (4 points)
Part A:
Using the angle addition postulate, we know that the sum of angle BAC and angle CAD is equal to angle BAD.
m∠BAC + m∠CAD = m∠BAD
(2x + 3) + (4x - 1) = 134
6x + 2 = 134
6x = 132
x = 22
Part B:
Now that we have found the value of x, we can substitute it back into the equation for m∠CAD.
m∠CAD = 4x - 1
m∠CAD = 4(22) - 1
m∠CAD = 88 - 1
m∠CAD = 87°
Therefore, the measure of angle CAD is 87°.