Using the angle relationships, determine the value of x in the diagram above.
(1 point)
Responses
x=25x is equal to 25
x=50x is equal to 50
x=55x is equal to 55
x=60
Since angles A and B form a straight line, their sum must be 180 degrees: A + B = 180. Thus, A = 180 - B.
Similarly, angles A and C are adjacent, so their sum must be 180 degrees as well: A + C = 180. Replacing A with 180 - B, we get (180 - B) + C = 180.
Simplifying the equation, we have C = B.
Since angle C and angle D are vertical angles, they must be congruent. Therefore, C = D.
Finally, since angle D and angle E are supplementary (they form a straight line), their sum must be 180 degrees: D + E = 180.
Substituting C for D, we get C + E = 180.
We can set up the following equations:
B = C
C + E = 180
From the given answer choices, x=55 satisfies these equations.
Using the angle relationships, determine the value of y in the diagram above.
(1 point)
Responses
y=15y is equal to 15
y=30y is equal to 30
y=45y is equal to 45
y=90
Without access to the actual diagram, it is not possible to determine the value of y. The information provided in the question is insufficient to determine the value of y using angle relationships.
120 degrees
(2x + 10) degrees
(2y + 30) degrees
Based on the given information, we can determine the following relationship:
2x + 10 = 120
To solve for x, we can subtract 10 from both sides of the equation:
2x = 120 - 10
2x = 110
Finally, dividing both sides of the equation by 2 gives us:
x = 55
Therefore, the value of x is 55.