We are given:
- Parallelogram CDEF
- ∠C = 13x - 10
- ∠D = 5x + 10
To Find: ∠E
Concept Used:
- Adjacent angles of a Parallelogram are Supplementary
Finding the value of 'x':
Since adjacent angles of a parallelogram are Supplementary:
∠D + ∠C = 180
5x + 10 + 13x - 10 = 180 [replacing the values of angle C and D]
18x = 180
x = 10 [dividing both sides by 18]
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Finding Measure of Angle D:
We are given that:
∠D = 5x + 10
∠D = 5(10) + 10 [since x = 10]
∠D = 60°
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Finding the measure of ∠E:
∠D and ∠E are Adjacent angles
Since Adjacent angles are Supplementary:
∠D + ∠E = 180
60 + ∠E = 180
∠E = 120° [subtracting 60 from both sides]
Hence, the measure of ∠E = 120°
Answer:
=8p−7.25
Step-by-step explanation:
=(5)(p)+(5)(−1)+(3)(p)+(3)(−0.75)
=5p+−5+3p+−2.25
=5p+−5+3p+−2.25
=(5p+3p)+(−5+−2.25)
=8p+−7.25
An equation has infinitely many solutions if it can be manipulated all the way to an identity (i.e. an equality where the right and left hand side are the same). We have:
A) 
which is impossible
B) 
which is an equality
C) 
which has a unique solution
D) 
which has a unique solution
