Answers are
Question 2
M/_ GBA = 34
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Question 2 is repeated so same answer
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Question 1
x = 9
y = 41
M/_ EBF = 56
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Step by step question 2
Triangle ABC will = 180
M/_ BCA is a vertical angle with 44*
So we know 180 - 102 - 44 = unknown 3rd angle BAC = 34
Alternate interior angle theory tells me BAC = GBA so GBA = 34
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Step by step question 1
I made a screen print to help
For solving for x, we know the top half of the circle is 180 degrees and the 3 angles will equal 90 degrees.
We know the 90 degree angle is 90.
So we add them in an equation.
90 + 3x + 7 + 5x + 11 = 180
Subtract 90 and 7 and 11 (108) from both sides to isolate variables
90 + 3x + 7 + 5x + 11 - 108 = 180 - 108
8x = 72
Divide both sides by 8 to solve for x
8/8 x = 72/8
X = 9
Now to solve for y
We know M/_ EBF is vertical and congruent with M/_ DBC ( 5x + 11)
Since we know the value of x = 9, we can substitute it for x in the equation for EBF.
(5)(9) + 11
M/_ EBF = 56
We know the two bottom angles (3y + 1) and (56) will equal to 180 degrees so we add them together for our equation
3y + 1 + 56 = 180
Subtract 56 + 1 (57) from both sides to isolate y
3y = 123
Divide both sides by 3 to solve for y
3/3 y = 123/3
y = 41
Check your work, substitute 41 for y in your equation
(3)(41) + 1 + 56 = 180
180 = 180
