Answer:
1st and 2nd statements are true.
Step-by-step explanation:
We are asked to choose the correct statements that can prove that quadrilateral DEFG is a parallelogram.
We will use parallelogram properties to answer this problem.
Since we know that a parallelogram has two sets of opposite angles congruent, therefore, 1st option is a correct choice.
Since a parallelogram has one set of opposite sides that are both congruent and parallel, therefore, second statement is true.
Since the consecutive angles of a parallelogram are supplementary, therefore, 3rd statement is not true.
Since the diagonals of parallelogram bisect each other, therefore, 4th statement is not true.
Answer:
G=7
Step-by-step explanation:
4(g-1)=24
4g-4=24
4g=28
g=7
Answer:
A is 55°
Step-by-step explanation:
To solve this, you need to remember that the sum of the angles inside a triangle is equal to 180 degrees.
Also, noting that this is an isosceles triangle. That means that a and b are equal. With that in mind, we can simply say:
a + b + c = 180
a ≡ b ∴ 2b + c = 180
2(4x + 31)° + (2x + 58)° = 180°
8x° + 62° + 2x° + 58° = 180°
Let's just stop right here, and note that normally you can treat symbols of measurements just like variables. We've done the same here, applying the distributive property with the ° symbol. Note though that it's currently part of every single term, so I'm going to factor it out:
(8x° + 62° + 2x° + 58°) / 1° = 180° / 1°
8x + 62 + 2x + 58 = 180
10x + 120 = 180
10x = 60
x = 6
Again noting that A and B are identical due to this being an Isosceles triangle, we can say:
A = (4x + 31)°
A = 24° + 31°
A = 55°
We can also check our answer. The sum of the angles should be 180, and two of those angles should be 55. That means that angle C should be 180 - 2 * 55, or 180 - 110 = 70. Let's test it:
70 = 2x + 58
70 = 12 + 58
70 = 70
So we know that our answer is correct.
3*4=12
2x*4=8x
So,answer is 8x+12
