Question

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

Answer 1

To find the value of x given that Ray AB bisects ∠CAT and the angle measures provided, we set up the equation 2x + 10 = 15 and solve for x, finding out that x equals 2.5.

Step-by-step explanation:

The question involves finding the value of x when we know that Ray AB bisects ∠CAT, and given m∠CAT = 30 degrees and m∠CAB = 2x + 10 degrees.

Since AB bisects ∠CAT, m∠CAT is divided into two equal angles of which ∠CAB is one part.

Therefore, m∠CAB would equal 30 degrees / 2 = 15 degrees.

Based on the given equation for m∠CAB, we can set 2x + 10 equal to 15 and solve for x.

2x + 10 = 15
2x = 5
x = 2.5

Answer 2

The value of x is 2.5.

From the diagram, we know that:

1. Ray AB bisects ∠CAT, which means it divides ∠CAT into two congruent angles.

2. Therefore, m∠CAB = m∠BAT.

3. We are also given that m∠CAT = 30 degrees.

4. We are given that m∠CAB = 2x + 10 degrees.

To find the value of x, we can use the following steps:

1. Since ∠CAB and ∠BAT are congruent, we can set their measures equal to each other:

m∠CAB = m∠BAT

2x + 10 = (1/2) * m∠CAT (because AB bisects ∠CAT)

2x + 10 = (1/2) * 30

2x + 10 = 15

2x = 5

x = 2.5