Find the,<ABC if the line BD bisects <ABC and given m<ABD = 5x and m<DBC = 3x + 10.
50 bro
Answers
true
false
supplementary
vertical
50
50
the answer is 50 not 5 i got it wrong
since BD bisects the angle, we must have]
5x = 3x+10
2x = 10
x = 5
So, you are correct, but that does not answer the question: What is <ABC?
You don't have to trust me but I am right for this year is correct, the answer is 50
sorry = my answer is 5
(x+15)
(4x-12)
Your mom is still correct
To find the measure of angle <ABC, we need to use the concept of angle bisectors.
An angle bisector is a line that divides an angle into two equal angles.
Given that line BD bisects angle <ABC, we can set the measures of angle ABD and angle DBC to be equal since they are the angles formed by the bisector.
So we have:
m<ABD = m<DBC
Setting the given expressions equal to each other:
5x = 3x + 10
Now, let's solve the equation to find the value of x:
5x - 3x = 10
2x = 10
Dividing both sides by 2:
x = 10/2
x = 5
Now that we have found the value of x, we can substitute it back into the expression for angle ABD to find its measure:
m<ABD = 5x
m<ABD = 5 * 5
m<ABD = 25
Since line BD bisects angle <ABC, angle <ABD and angle <DBC are equal. Therefore, the measure of angle <ABC is twice the measure of angle <ABD or angle <DBC:
m<ABC = 2 * m<ABD or m<ABC = 2 * m<DBC
m<ABC = 2 * 25
m<ABC = 50
Therefore, the measure of angle <ABC is 50 degrees.