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In the figure above, what is r + s in terms of x?

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A

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In the figure above, what is r + s in terms of x?

(A) x
(B) 2x
(C) 90 – x
(D) 90 – 2x
(E) 180 – 2x

Attachment:

2017-08-22_1947.png [ 6.77 KiB | Viewed 2150 times ]

Official Answer

A

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Clearly answer is A : x
solution is attached.

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IMG_0732.JPG [ 1.68 MiB | Viewed 1927 times ]

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(90-x)+s+r+90=180

180-x+r+s=180
r+s=x

Answer A

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Bunuel

In the figure above, what is r + s in terms of x?

(A) x
(B) 2x
(C) 90 – x
(D) 90 – 2x
(E) 180 – 2x

Attachment:

2017-08-22_1947.png

Angles sum to 180

\(r + s + (90 - x) + 90 = 180\)

\(r + s + 90 - x + 90 = 180\)

\(r + s - x = 0\)

\(r + s = x\)

Answer A

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Bunuel

In the figure above, what is r + s in terms of x?

(A) x
(B) 2x
(C) 90 – x
(D) 90 – 2x
(E) 180 – 2x

Attachment:

2017-08-22_1947.png

The third angle in triangle that contains right angle and (90-x) is
180 - 90 -(90-x)
= x

r+s= x since exterior angle is equal to sum of interior opposite angles

Answer A

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Bunuel

In the figure above, what is r + s in terms of x?

(A) x
(B) 2x
(C) 90 – x
(D) 90 – 2x
(E) 180 – 2x

Attachment:

2017-08-22_1947.png

The large right triangle has 180 degrees. We can create the following equation:

r + s + (90 - x) + 90 = 180

r + s - x + 180 = 180

r + s - x = 0

r + s = x

Answer: A

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