Thankfully, we are given that ray AB “BISECTS” angle CAD. Bisect means to divide into two equal parts. I would’ve guessed angle CAD is complementary if not for that word. So if ray AD bisects angle CAD, and angle CAB equals 33 degrees, then angle BAD must also equal 33 degrees.
So let’s solve for x first:
4x + 1 = 33
Subtract 1 to both sides:
4x = 32
Divide both sides by 4:
x = 8
There’s the first answer, x equals 8.
Now we need to find the measure of angle CAD, which is equal to angle CAB (33 degrees) plus angle BAD ([4x+1] degrees). We can simply add them up, but first, we have to solve for angle BAD:
4x + 1
Plug in x value (solved and got 8):
4(8) + 1
Multiply:
32 + 1
Add:
33
Angle BAD equals 33 degrees, which makes sense. Because it should be 33 degrees, since ray AB “BISECTS” angle CAD. Angle BAD AND CAB should both be equal to each other.
Now that we have the angle measures of the two angles, we just have to add them up to find angle CAB:
33 + 33
Add:
66
Angle CAD is 66 degrees.
Hope this step by step and detailed explanations helped!