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In the following figure, what is the measure of x?

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Farina
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In the following figure, what is the measure of x? [#permalink] New post   03 Aug 2020, 00:55
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In the following figure, what is the measure of x?

A. 30
B. 45
C. 60
D. 75
E. 90

Quant Sec 7
ID: Q02-10
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D

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Re: In the following figure, what is the measure of x? [#permalink] New post   03 Aug 2020, 04:09
The triangle to the left with all sides 5 is an equilateral triangle will have all angles 60.
The triangle to the right is a right triangle which satisfies the Pythagorean theorem and since the two sides are 5 the opp. angles are equal, making them 45 degrees each.
The third triangle in the centre (with no measurements of the sides) will have angles 45, 60 and x (applying the property that when two lines intersect the pair opp. angles are equal)

Therefore, x + 45 + 60 = 180. So, x= 75.
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Re: In the following figure, what is the measure of x? [#permalink] New post   03 Aug 2020, 05:22
Aaka wrote:
The triangle to the left with all sides 5 is an equilateral triangle will have all angles 60.
The triangle to the right is a right triangle which satisfies the Pythagorean theorem and since the two sides are 5 the opp. angles are equal, making them 45 degrees each.
The third triangle in the centre (with no measurements of the sides) will have angles 45, 60 and x (applying the property that when two lines intersect the pair opp. angles are equal)

Therefore, x + 45 + 60 = 180. So, x= 75.


Hi,
Thank you very much for the explanation. If possible for you, kindly explain with picture or if someone else can do that.
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Re: In the following figure, what is the measure of x? [#permalink] New post   03 Aug 2020, 06:23
1
Farina wrote:
Aaka wrote:
The triangle to the left with all sides 5 is an equilateral triangle will have all angles 60.
The triangle to the right is a right triangle which satisfies the Pythagorean theorem and since the two sides are 5 the opp. angles are equal, making them 45 degrees each.
The third triangle in the centre (with no measurements of the sides) will have angles 45, 60 and x (applying the property that when two lines intersect the pair opp. angles are equal)

Therefore, x + 45 + 60 = 180. So, x= 75.


Hi,
Thank you very much for the explanation. If possible for you, kindly explain with picture or if someone else can do that.

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Re: In the following figure, what is the measure of x? [#permalink] New post   03 Aug 2020, 06:36
Aaka wrote:
Farina wrote:
Aaka wrote:
The triangle to the left with all sides 5 is an equilateral triangle will have all angles 60.
The triangle to the right is a right triangle which satisfies the Pythagorean theorem and since the two sides are 5 the opp. angles are equal, making them 45 degrees each.
The third triangle in the centre (with no measurements of the sides) will have angles 45, 60 and x (applying the property that when two lines intersect the pair opp. angles are equal)

Therefore, x + 45 + 60 = 180. So, x= 75.


Hi,
Thank you very much for the explanation. If possible for you, kindly explain with picture or if someone else can do that.


Much Appreciated. Now its clear
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Re: In the following figure, what is the measure of x? [#permalink]
03 Aug 2020, 06:36
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