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Tpy6a [65]
3 years ago
8

If the measure of angle BCD=51 degrees, solve for x.

Mathematics
1 answer:
BabaBlast [244]3 years ago
4 0

Answer:

x=5

Step-by-step explanation:

step 1

Find the measure of angle EFD

In this problem I will assume that ABCD is a parallelogram

In a parallelogram opposite angles are congruent and consecutive angles are supplementary

so

m\ angle BCD=m\angle BED=51^o

m\ angle FED=(1/2)m\angle BED=(1/2)51^o=25.5^o --- > given problem

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

In the triangle EFD

m\ angle FED+m\ angle FDE+m\ angle EFD=180^o

substitute the given values

25.5^o+55^o+m\ angle EFD=180^o

80.5^o+m\ angle EFD=180^o

m\ angle EFD=180^o-80.5^o

m\ angle EFD=99.5^o

step 2

Find the measure of angle EFB

we know that

m\angle EFB+m\angle EFD=180^o ---> by supplementary angles

we have

m\ angle EFD=99.5^o

substitute

m\angle EFB+99.5^o=180^o

m\angle EFB=180^o-99.5^o

m\angle EFB=80.5^o

step 3

Find the value of x

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

In the triangle EBF

m\ angle BEF+m\ angle EFB+m\ angle EBF=180^o

we have

m\angle BEF=m\ angle FED=25.5^o

m\angle EFB=80.5^o

m\angle EBF=(14x+4)^o

substitute

25.5^o+80.5^o+(14x+4)^o=180^o

solve for x

Combine like terms

(14x+110)^o=180^o

14x=180-110

14x=70

x=5

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