Answer:
The given quadrilateral is a parallelogram.
Step-by-step explanation:
If a quadrilateral is a parallelogram , then the opposite sides would be equal.
Here we are going to equate the length of 1 pair of opposite sides to find the value of x and use this value of x to verify whether the other pair of opposite sides are equal.
AB = 6x
BC = 3x
DC = x + 15
AD = 9
Equate AB and CD,
6x = x + 15
5x = 15
x = 3
Now BC and DA should be equal.
BC = 3x = 9
Also DA = 9
As we can see, the other pair of opposite sides are also equal.
Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent.
Hence , the given quadrilateral is a parallelogram.
It is parallel due to the fact that it is the exact same number with one being positive and one being negative.
144 is the answer to 12x12
Answer:
m∠1 = 63°
m∠2 = 49°
m∠3 = 87°
m∠4 = 44°
Step-by-step explanation:
From the given figure
∵ ∠2 and 49° are vertically opposite angles
∵ The vertical opposite angles are equal in measures
∴ m∠2 = 49°
∵ The sum of the interior angles of a Δ is 180°
∵ m∠1, m∠2, and 68° are interior angles of a Δ
∴ m∠1 + m∠2 + 68° = 180°
∵ m∠2 = 49°
∴ m∠1 + 49° + 68° = 180°
→ Add the like terms in the left side
∴ m∠1 + 117 = 180
→ Subtract 180 from both sides
∴ m∠1 = 63°
∵ ∠3 and 93° formed a pair of linear angles
∵ The sum of the measures of the linear angles is 180°
∴ m∠3 + 93° = 180°
→ Subtract 93 from both sides
∴ m∠3 = 87°
∵ 93° is an exterior angle of the triangle
∵ The measure of the exterior angle of a Δ at one vertex equals the sum
of the measures of the opposite interior angles to this vertex
∵ ∠4 and 49° are the opposite interior angles to 93°
∴ 49° + m∠4 = 93°
→ Subtract 49 from both sides
∴ m∠4 = 44°
I believe it is the commutative property of multiplication. Commutative property is you can put the numbers in any order and it will have the same end result. I got multiplication because it is multiplication.
Hope this helps!
