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In the diagram above, lines EF and DE are each tangent to the circle.

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Bunuel
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In the diagram above, lines EF and DE are each tangent to the circle. [#permalink] New post   02 Mar 2015, 08:29
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A
B
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E

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5% (low)

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90% (01:06) correct 10% (01:38) wrong based on 135 sessions
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In the diagram above, lines EF and DE are each tangent to the circle. If ∠FOD = 110°, what is the measure of ∠DEF?

A. 40°
B. 50°
C. 60°
D. 70°
E. 80°

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D
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peachfuzz
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Re: In the diagram above, lines EF and DE are each tangent to the circle. [#permalink] New post   02 Mar 2015, 19:19
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Bunuel wrote:
Attachment:
c3_img4.png
In the diagram above, lines EF and DE are each tangent to the circle. If ∠FOD = 110°, what is the measure of ∠DEF?

A. 40°
B. 50°
C. 60°
D. 70°
E. 80°

Kudos for a correct solution.


Sum of interior angles for a polygon is 180(n-2)

Polygon FODE have interior angles that sum to 360 degrees.

360-180-110=70

Answer: D
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Re: In the diagram above, lines EF and DE are each tangent to the circle. [#permalink] New post   02 Mar 2015, 22:12
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Answer = D = 70

Refer diagram below:

Attachment:
c3_img4.png
c3_img4.png [ 14.43 KiB | Viewed 3334 times ]


Both lines are tangent, so angles = 90 degrees

∠DEF = 180 - ∠FOD = 180-110 = 70
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Bunuel
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In the diagram above, lines EF and DE are each tangent to the circle. [#permalink] New post   08 Mar 2015, 14:09
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Bunuel wrote:

In the diagram above, lines EF and DE are each tangent to the circle. If ∠FOD = 110°, what is the measure of ∠DEF?

A. 40°
B. 50°
C. 60°
D. 70°
E. 80°

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

We are told that ∠FOD = 110°, and we know that ∠EFO = ∠EDO = 90°, because those two lines are tangent lines. Now look at quadrilateral ODEF. We know that the sum of the four angles of any quadrilateral has to equal 360°.
∠EFO + ∠EDO + ∠FOD + ∠ DEF = 360°
90° + 90° + 110° + ∠ DEF = 360°
290° + ∠ DEF = 360°
∠ DEF = 360° – 290° = 70°.

Answer = D
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Re: In the diagram above, lines EF and DE are each tangent to the circle. [#permalink] New post   09 Mar 2015, 06:24
The main properties tested here are:

- a radius connected to a tangent forms a 90 degree angle
- sum of angles in a quadrilateral, or any polygon for that matter. Sum of angles = (#sides-3)*180

if you know these properties, you can solve the problem easily.

110+90+90 = 290.

360-290 = 70 degrees.

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Re: In the diagram above, lines EF and DE are each tangent to the circle. [#permalink] New post   05 Jul 2017, 19:23
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Re: In the diagram above, lines EF and DE are each tangent to the circle. [#permalink]
05 Jul 2017, 19:23
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