Question

Ray AB bisects ∠CAT. If m∠CAT = 30 and m∠CAB = 2x + 10 then give the value of x.

Answer 1

The measure of ∠CAB is the same as ∠CAT since ray AB bisects ∠CAT, and by solving the equation 2x + 10 = 15, we find that x = 2.5.

Step-by-step explanation:

The student is asking about finding the value of x in a geometric problem involving angle bisectors. Since ray AB bisects ∠CAT and the measure of ∠CAT is given as 30 degrees, it implies that both angles created by the bisection have equal measures. Thus, the measure of ∠CAB (which is one of the two angles) is also 15 degrees.

Given that the measure of ∠CAB is also expressed as 2x + 10, we can create an equation 2x + 10 = 15.

Now we solve for x:

1. 2x + 10 = 15
2. 2x = 15 - 10
3. 2x = 5
4. x = 5 / 2
5. x = 2.5

The value of x is 2.5.