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# The vertex angle of an isosceles is p degrees. How many degrees are th

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Math Expert
Joined: 02 Sep 2009
Posts: 58414
The vertex angle of an isosceles is p degrees. How many degrees are th  [#permalink]

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19 Mar 2018, 01:22
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25% (medium)

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80% (00:38) correct 20% (00:44) wrong based on 36 sessions

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The vertex angle of an isosceles is p degrees. How many degrees are there in one of the base angles?

A. 180 - p
B. 90 - p
C. 180 - 2p
D. 180 - p/2
E. 90 - p/2

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Re: The vertex angle of an isosceles is p degrees. How many degrees are th  [#permalink]

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19 Mar 2018, 01:25
Bunuel wrote:
The vertex angle of an isosceles is p degrees. How many degrees are there in one of the base angles?

A. 180 - p
B. 90 - p
C. 180 - 2p
D. 180 - p/2
E. 90 - p/2

As the calculation required is straightforward, we'll just do it.
This is a Precise approach.

Since the vertex degree is p, then the other two angles (the base angles) sum to 180 - p.
Since the base angles of an isosceles are equal, each is equal to (180 - p)/2 = 90 - p/2

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Re: The vertex angle of an isosceles is p degrees. How many degrees are th  [#permalink]

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19 Mar 2018, 01:29
Bunuel wrote:
The vertex angle of an isosceles is p degrees. How many degrees are there in one of the base angles?

A. 180 - p
B. 90 - p
C. 180 - 2p
D. 180 - p/2
E. 90 - p/2

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Re: The vertex angle of an isosceles is p degrees. How many degrees are th  [#permalink]

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19 Mar 2018, 04:41
Vertex angle= p
Sum of other two angles= 180-p

Triangle is isosceles. So other two angles are equal.

Measure of one angle= $$\frac{180-p}{2}$$= 90-$$\frac{p}{2}$$

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Re: The vertex angle of an isosceles is p degrees. How many degrees are th  [#permalink]

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20 Mar 2018, 16:53
Bunuel wrote:
The vertex angle of an isosceles is p degrees. How many degrees are there in one of the base angles?

A. 180 - p
B. 90 - p
C. 180 - 2p
D. 180 - p/2
E. 90 - p/2

Since the base angles of an isosceles triangle are equal, we can let b = the measure of a base angle of the triangle and create the equation:

2b + p = 180

2b = 180 - p

b = (180 - p)/2

b = 90 - p/2

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Re: The vertex angle of an isosceles is p degrees. How many degrees are th   [#permalink] 20 Mar 2018, 16:53
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