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505-555 (Easy)|   Geometry|      
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Bunuel
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In the figure above, what does x + y equal? 22 May 2020, 06:27
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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15% (low)

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78% (01:17) correct 22% (01:03) wrong based on 218 sessions

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In the figure above, what does x + y equal?

A. 315
B. 270
C. 225
D. 180
E. It cannot be determined from the information given.


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B
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In the figure above, what does x + y equal? 22 May 2020, 06:40
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Bunuel

In the figure above, what does x + y equal?

A. 315
B. 270
C. 225
D. 180
E. It cannot be determined from the information given.


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Solution


    • Using the properties of straight angle, we can write the two angles of the triangle as below:

    • Since, in a triangle, the sum of all three interior angles = 180°
      o This means, 90° + (180 – x)° + (180 -y)° = 180°
        ⟹ x+ y = 270
Thus, the correct answer is Option B.
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In the figure above, what does x + y equal? 22 May 2020, 06:42
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In the figure above, what does x + y equal?

A. 315
B. 270 --> correct: (180-x)+(180-y)=90 => x+y=360-90=270
C. 225
D. 180
E. It cannot be determined from the information given.
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In the figure above, what does x + y equal? 22 May 2020, 07:02
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Bunuel

In the figure above, what does x + y equal?

A. 315
B. 270
C. 225
D. 180
E. It cannot be determined from the information given.


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Let's add two additional angles to the triangle to get:


Since angles in a triangle add to 180°, we can write: a + b+ 90 = 180
Subtract 90° from both sides of the equation to get: a + b = 90

Since angles on a line add to 180 degrees, we can write: x + a = 180
Subtract a from both sides to get: x = 180 - a

Likewise, y + b = 180
Subtract b from both sides to get: y = 180 - b

What does x + y equal?
x + y = (180 - a) + (180 - b)
= 360 - a - b
= 360 - (a + b)
= 360 - (90)
= 270

Answer: B

Cheers,
Brent
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In the figure above, what does x + y equal? 22 May 2020, 07:10
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Bunuel

In the figure above, what does x + y equal?

A. 315
B. 270
C. 225
D. 180
E. It cannot be determined from the information given.


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((180-x) + (180-y) = 90

i.e. x+y = 270

Answer: Option B
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In the figure above, what does x + y equal? 10 Aug 2022, 04:25
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