To solve this problem, we need to use the theorem which states that the sum of angles in a triangle is equal to 180 degrees. The value of m<FED is equal to 120 degrees. From the diagram given, m<CBD is complimentary with m<BED
Sum of Angles in a Triangle
The value of m<FED can be calculated by summing the entire entity and equating to 180 degrees.
Data;
- m<FED = (16x - 8)
- m<EFD = 35
- m<EDF = 2x + 9
[tex]35+(16x-8)+(2x+9) = 180[/tex]
Reason: The sum of angles in a triangle is equal to 180 degrees.
But we would need to solve for the value of x.
[tex]35+(16x-8)+(2x+9) = 180\\35 + 16x - 8 + 2x + 9 = 180\\36+ 18x = 180\\180 - 36 = 18x\\18x = 144\\x = \frac{144}{18} \\x = 8[/tex]
Let's substitute the value of x into m<FED
[tex]m < FED = 16x - 8\\x = 8\\m < FED = 16(8) - 8 \\m < FED = 128 - 8\\m < FED = 120^0[/tex]
The value of m<FED is equal to 120 degrees.
From the diagram given, m<CBD is complimentary with m<BED
Learn more on sum of angles in a triangle here;
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