Question

What is the m∠DBC?

60

120

30

45

Answer 1

do you know what angle DBA=?

Answer 2

180?

Answer 3

how?

Answer 4

the total of ALL angles in any triangle is 180

Answer 5

because all sides are equal

Answer 6

so one of the angles canot be 180

Answer 7

so dbc is 120

Answer 8

triangle ABD is an equilateral triangle - so all angles are equal

Answer 9

what is each angle of an equilateral triangle equal to?

Answer 10

60

Answer 11

correct - so that means angle DBA=60

agreed?

Answer 12

yes

Answer 13

and similarly:

angle BDA=60

Answer 14

now note that angle BDA is an external angle of triangle BCD

Answer 15

so this means:

BDA = DBC + DCB

agreed?

Answer 16

yes

Answer 17

so 60+60 is 120

Answer 18

also note that triangle BCD is an isosceles triangle

Answer 19

which means angle DBC=BCD

Answer 20

yes

Answer 21

so we can say:

BDA = DBC + DCB = DBC + DBC (because DCB=DBC)
= 2 * DBC

therefore:

DBC = BDA/2

Answer 22

so its 120

Answer 23

:/

Answer 24

look further up - what did we say BDA=?

Answer 25

DBC which is 60

Answer 26

no

Answer 27

we said BDA=DBA=DAB=60

and we have shown that:

DBC = BDA/2

Answer 28

oh 30

Answer 29

yes :)

Answer 30

yessss thanks so much im def becoming a fan

Answer 31

yw - and thanks! :D