1. If LMNO is a parallelogram, and LM=2y-9 and NO=y-2, find the value of 'y'.

Does y=7?

2. RSTV is a parallelogram. RT and SV intersect at Q. RQ=5x+1 and QT=3x+15. Find OT.
Does QT=7?

3. RATS is a parallelogram. If angle s= (8x) and angle t=(7x) then find the value of 'x'.
Does x=12?

4. In triangleABC, AB=3, BC=4 and AC=6. Name the largest angle.
Is the largest angle B?

5. Find the sum of the interior angles of a decagon.
Is the sum 144?

#1 ok

#2 ok
#3 ok
#4 ok
#5 8(180) = 1440
each angle is 144, not the sum.

1. To find the value of 'y' in the parallelogram LMNO, we need to set the opposite sides equal to each other. Since LMNO is a parallelogram, LM = NO.

So, 2y - 9 = y - 2.

To solve this equation, you can subtract 'y' from both sides: 2y - y - 9 = y - y - 2, which simplifies to y - 9 = -2.

Next, add 9 to both sides: y - 9 + 9 = -2 + 9, which gives y = 7.

Therefore, the value of 'y' is indeed 7.

2. To find the length of OT in parallelogram RSTV, we can use the fact that the opposite sides of a parallelogram are equal. OT is opposite to RQ, so TO = RQ.

Given that RQ = 5x + 1, we can substitute this value into the equation TO = RQ: OT = 5x + 1.

Therefore, the length of OT is 5x + 1, not necessarily equal to 7.

3. In parallelogram RATS, the opposite angles are congruent. Therefore, angle s = angle t.

Given that angle s = 8x and angle t = 7x, we can set them equal to each other: 8x = 7x.

To solve for 'x', subtract 7x from both sides: 8x - 7x = 7x - 7x, which simplifies to x = 0.

Therefore, the value of 'x' is 0, not equal to 12.

4. In triangle ABC, the largest angle can be found using the Law of Cosines. Given the lengths of the sides AB, BC, and AC, we can use the formula:

AC^2 = AB^2 + BC^2 - 2(AB)(BC) * cos(angle C).

Substituting the values, we get:

6^2 = 3^2 + 4^2 - 2(3)(4) * cos(angle C).

Simplifying further:

36 = 9 + 16 - 24 * cos(angle C).

Continuing the simplification:

36 = 25 - 24 * cos(angle C).

To solve for the cosine of angle C, subtract 25 from both sides: 36 - 25 = -24 * cos(angle C), which gives 11 = -24 * cos(angle C).

Since a cosine value cannot be greater than 1 or less than -1, it is not possible for 11 to be equal to -24 * cos(angle C).

Therefore, the largest angle in triangle ABC cannot be angle B.

5. The sum of the interior angles of a decagon can be found using the formula:

Sum of interior angles = (n - 2) * 180 degrees.

Substituting the value of n=10 (since a decagon has 10 sides):

Sum of interior angles = (10 - 2) * 180 degrees.

Simplifying further:

Sum of interior angles = 8 * 180 degrees = 1440 degrees.

Therefore, the sum of the interior angles of a decagon is indeed 1440 degrees, not equal to 144.

1. If LMNO is a parallelogram, then opposite sides are equal. Therefore, LM = ON.

Given:
LM = 2y - 9
ON = y - 2

Setting up the equation:
2y - 9 = y - 2

Simplifying the equation:
2y - y = -2 + 9
y = 7

Therefore, y = 7.

2. In a parallelogram, the opposite sides are equal. Therefore, RQ = SV.

Given:
RQ = 5x + 1
QT = 3x + 15

We need to find OT. Since OT is a diagonal, we will add the lengths of RQ and QT to get OT.

OT = RQ + QT
OT = (5x + 1) + (3x + 15)
OT = 5x + 1 + 3x + 15
OT = 8x + 16

Therefore, OT = 8x + 16.

3. In a parallelogram, opposite angles are equal. Therefore, angle R = angle S.

Given:
angle S = 8x
angle T = 7x

We need to find the value of x.

Since angle R = angle S, we can set up the equation:
8x = 7x

Simplifying the equation:
8x - 7x = 0
x = 0

Therefore, x = 0.

4. In a triangle, the largest angle is opposite the longest side. Given that AB = 3, BC = 4, and AC = 6, the longest side is AC.

Therefore, the largest angle is opposite side AC.

So, the largest angle in triangle ABC is angle C.

5. The sum of the interior angles of a polygon can be calculated using the formula:

Sum = (n-2) * 180 degrees

Where n is the number of sides of the polygon.

For a decagon, n = 10.

Substituting the value of n into the formula:
Sum = (10-2) * 180
Sum = 8 * 180
Sum = 1440

Therefore, the sum of the interior angles of a decagon is 1440 degrees.