Question

Given that BD=BC, find B.

A. 54
B. 57
C. 65
D. 66

Answer 1

@mathstudent55

Answer 2

OHHH I GOT IS

Answer 3

I mean, CD gives me 11.

Answer 4

i think

Answer 5

Here you use the converse of the other theorem.
In a triangle, if two sides are congruent, then their opposite angles are congruent.

Answer 6

i think u set point C equal to D

Answer 7

Since you know those two angles are congruent, set one equal to the other and solve for x.
What do you get for x?

Answer 8

How do I set it up?

Answer 9

We know nothing about the sides. All we know is angle measures.

Answer 10

6x - 9 = 3x + 24

Solve for x.

What do you get for x?

Answer 11

11

Answer 12

Great.
Now plug in 11 into x in either
6x - 9
or in
3x + 24
What do you get?

Answer 13

Aaaah, 57

Answer 14

Thank you so much math

Answer 15

Not so fast. We're not done yet.

Answer 16

Now we know that the measures of angles C and D are 57.
The question is what is the measure of angle B?

Answer 17

Oh

Answer 18

What do you know about the sum of the measures of the angles of a triangle?

Answer 19

They're all equal

Answer 20

I mean they contain 180 degrees

Answer 21

No. Your answer does not answer my question.
See the figure below:

Answer 22

Ok, that's better.
In my figure, a + b + c = 180, right?

Answer 23

Right

Answer 24

So, 66.

Answer 25

Ok, now your problem, again.



57 + 57 + x = 180

114 + x = 180

x = 180 - 114

x = 66

Answer 26

You are correct.

Answer 27

Thank you!!

Answer 28

B = 66

Answer 29

I almost put 57 too

Answer 30

The problem is trying to trick you, but you're smarter than the trick.

Answer 31

You're welcome.