Data Sufficiency

Is the degree measure of one of the angles of quadrilateral ABCD equal to 60 degree ?

1. Two of the Interior angels of ABCD are Right angles
2. The degree measure of angle ABC is twice the degree measure of angle BCD

Statement 1 is sufficient
Statement 2 is sufficient
Statement 1 and Statement 2 togethet are sufficient
Either Statement alone is sufficient
Neither Statment is sufficient

Can you please confirm the answer.

anks17 wrote:Is the degree measure of one of the angles of quadrilateral ABCD equal to 60 degree ?

1. Two of the Interior angels of ABCD are Right angles
2. The degree measure of angle ABC is twice the degree measure of angle BCD

Can you please confirm the answer.

We have quadrilateral ABCD. We need to find if any angle is 60. Lets check the statements.


1. Two of the Interior angels of ABCD are Right angles
Only two angles are right angles. The other two angles can be 90-90, 60-120, 50-130 etc. Insufficient.

2. The degree measure of angle ABC is twice the degree measure of angle BCD
ABC is twice BCD, clearly the four angles can be pretty much anything. Insufficient.

Together:
1. If ABC = 90, BCD = 45, the other two angles are 90-135.
2. If ABC=120, BCD =60, the other two angles are 90-90.
So even though we narrowed it down to 2 choices, its still 2 valid choices. We can't select one or the other.
Still Insufficient.

E is correct.


PS: If you want to visualize it or draw it out, think of a right angled trapezium.

Thanks eagleeye. While solving question just thought that 90 + 90 + 2x + x= 360 and Thus x=60 and hence chose option C as answer. Didn't think about the combination of angles can be 90, 45, 135, 90 that also satisfies both the conditions. How did you think about that ? Can you plz give some tips that we do not overlook such scenarios that can lead to a different answer than obvious.

anks17 wrote:Thanks eagleeye. While solving question just thought that 90 + 90 + 2x + x= 360 and Thus x=60 and hence chose option C as answer. Didn't think about the combination of angles can be 90, 45, 135, 90 that also satisfies both the conditions. How did you think about that ? Can you plz give some tips that we do not overlook such scenarios that can lead to a different answer than obvious.

Geometry DS questions mostly require drawing the problem on paper. A couple of things that can help:
1. Vivid visualization and quantity of practice.
2. More importantly, intimate familiarity with different types of such geometric figures as standard triangles, different kinds of quadrilaterals, etc.

This post may be helpful in understanding different types of quadrilaterals.

https://www.beatthegmat.com/need-help-on ... 15823.html