Geometry 3

[phoenix9801]

I am sure of my answer was correct and unfortunately the material does not provide any solution. So I was wondering if someone can help me please. Thank You

[eagleeye]

Hi phoenix9801:

Since these questions are really easy and you are only looking for answers, I will provide what I found, use these to check your answers.

[spoiler]x=60
[/spoiler]
Let me know if this helps

[Anurag@Gurome]

Question 1:
As AE = BD and C is the midpoint of both AE and BD, AC = BC.
Hence, ABC is an isosceles triangle.
Hence, angle ABC = angle BAC

Now, measure of angle BCE is 120°
Hence, measure of angle BCA is (180° - 120°) = 60°

Therefore, measure of angle BAC = measure of angle ABC = (180° - 60°)/2 = 60°

Hence, x = 60

The correct answer is D.

[Anurag@Gurome]

Question 2:


Refer to the above figure.
Measure of the angles marked by red = n° = 60°
And measure of the sum of the angles marked by blue = (180° - p°) + (180° - q°) + (180° - r°) = 540° - (p° + q° + r°)

Now, measure of the sum of the angles of the quadrilateral = Measure of the angles marked by red + Measure of the sum of the angles marked by blue = 360°

Hence, [60° + 540° - (p° + q° + r°)] = 360°
Hence, (p° + q° + r°) = 60° + 540° - 360° = 600° - 360° = 240°

The correct answer is B.

[bubbliiiiiiii]

Hence, [120° + 540° - (p° + q° + r°)] = 360°
Hence, (p° + q° + r°) = 120° + 540° - 360° = 660° - 360° = 300°

I think there was a typo?

Since n=60, the angle in red is 60 (not 120).

The equation changes accordingly,

Hence, [60° + 540° - (p° + q° + r°)] = 360°
Hence, (p° + q° + r°) = 60° + 540° - 360° = 600° - 360° = 240°

Please correct if I am wrong.

[Anurag@Gurome]

Thanks for pointing it out.
Edited the reply.