Question

Help with number 24, please explain!!

Answer 1

Answers for problem 24:

Angle EBG = 16 degrees

Angle BGC = 58 degrees

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Step-by-step explanation:

Let

x = measure of angle EBG

y = measure of angle EGB

z = measure of angle BGC

Angle ABF = 74, angle FBG = 90, and angle EBG = x all combine to form a straight angle which is 180 degrees. Add these angles up, set the sum equal to 180, and solve for x

(angle ABF)+(angle FBG) + (angle EBG) = 180

74+90+x = 180

164+x = 180

164+x-164 = 180-164 ... subtract 164 from both sides

x = 16

Therefore angle EBG is 16 degrees

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Now focus on triangle BEG. We found angle B to be 16 degrees (this was angle EBG). Angle E is given to be 42. Angle G is unknown which I've defined with the variable y. The three angles of any triangle add to 180

B+E+G = 180

16+42+y = 180

58+y = 180

58+y-58 = 180-58 .... subtract 58 from both sides

y = 122

Therefore, angle EGB is 122 degrees

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Use the value of y to find z. The two angles y and z add to 180 (they form a straight angle), so,

y+z = 180

z = 180-y

z = 180-122 .... replace y with 122

z = 58

Therefore, angle BGC is 58 degrees

Answer 2

ABE is a straight line = 180 degrees. FBG = 90 degrees, and ABF = 74. 180-90-74=16 degrees for angle GBE. A triangle equals 180 degrees subtract the 16 and 42 from 180 and the answer would be 122 degrees for angle BGE.