Question

PLEASE HELP MEEE

1st pic. Referring to the figure, given ray BD bisects ∠ABC,
find the value of x.

2nd pic. Referring to the figure, given ray BD bisects ∠ABC,
find the value of x.

Given ∠A and ∠B are supplementary. The measure
of ∠B is three times the measure of ∠A. Find m∠A.

Given ∠A and ∠B are supplementary. The measure
of ∠B is three times the measure of ∠A. Find m∠B.

Answer 1

Refer to the explanation for the answer!

Explanation:

Hello! Here is what I've found:

<ABC and <DBC in the first picture are both 30 degrees.

<ABC and <DBC in the second picture are both 10 degrees.

For m<A: It would be <A = x and <B = 3x

For m<B: It would be <A = 3x and <B = x

Answer 2

x1=15, x2=10, angle A=45, angle B=135

Explanation:

1st pic: since ray BD bisects angle ABC, 2x=x+15, subtract x from both sides to get x=15

2nd pic: using the same logic as above, x=4x-30. add 30 and subtract x from both sides to get 3x=30, divide by 3 to get x=10

since angle A and angle B are supplementary, A+B=180, since B=3A, we have A+3A=180, or 4A=180. divide to get A=45. since B=3A, B=3*45=135