Two consecutive angles of a parallelogram measures (X+35) and (5X-21) respectively determine the measures of each angle in the parallelogram.
x+35 + 5x-21 =180
Ah, the parallelogram, the shape that's just too cool for corners. Let's solve this like champions.
We know that opposite angles in a parallelogram are congruent. So, we can set up the equation:
(X + 35) = (5X - 21)
Now, let's solve it and find the value of our precious 'X'.
X + 35 = 5X - 21
Subtract X from both sides:
35 = 4X - 21
Add 21 to both sides:
56 = 4X
Divide both sides by 4:
X = 14
Now that we know 'X' is 14, we can find the measures of the angles:
First angle: (X + 35) = (14 + 35) = 49 degrees
Second angle: (5X - 21) = (5 * 14 - 21) = 49 degrees
So, each angle in the parallelogram measures 49 degrees. It's always nice to have equal angles, it keeps everything fair and square!
To find the measures of the angles in the parallelogram, we need to use the property that opposite angles in a parallelogram are equal.
Let's denote the consecutive angles as A and B.
According to the problem, angle A measures (X + 35), and angle B measures (5X - 21).
Since angle A and angle B are consecutive, they are opposite to each other in the parallelogram, so they are equal.
Setting up the equation:
(X + 35) = (5X - 21)
Now, let's solve this equation to find the value of X:
X + 35 = 5X - 21
Combine like terms:
4X + 35 = -21
Subtract 35 from both sides:
4X = -21 - 35
4X = -56
Divide both sides by 4:
X = -56 / 4
X = -14
Now that we have the value of X, we can substitute it back into the expressions for angle A and angle B:
Angle A = X + 35 = -14 + 35 = 21 degrees
Angle B = 5X - 21 = 5(-14) - 21 = -70 - 21 = -91 degrees
So, the measures of the angles in the parallelogram are:
Angle A = 21 degrees
Angle B = -91 degrees
To determine the measures of each angle in the parallelogram, we need to set up an equation based on the given information. Let's call the two consecutive angles A and B.
According to the given information, the measure of angle A is represented as (X + 35), and the measure of angle B is represented as (5X - 21).
Since the opposite angles in a parallelogram are equal, we can set up the equation:
A = B
Substituting the values of the angles, we get:
(X + 35) = (5X - 21)
Now we can solve this equation to find the value of X. Then we can substitute that value back into the expressions for A and B to determine their measures.
Let's solve the equation:
(X + 35) = (5X - 21)
First, we can simplify by expanding the brackets:
X + 35 = 5X - 21
Next, we can simplify by moving all the X terms to one side of the equation and the constant terms to the other side:
X - 5X = -21 - 35
Combine like terms:
-4X = -56
To isolate X, we divide both sides of the equation by -4:
X = -56 / -4
Simplifying further:
X = 14
Now that we have the value of X, we can substitute it back into the expressions for A and B to find their measures.
For angle A:
A = (X + 35)
A = (14 + 35)
A = 49
For angle B:
B = (5X - 21)
B = (5 * 14 - 21)
B = 69
Therefore, in the parallelogram, the measure of angle A is 49 degrees, and the measure of angle B is 69 degrees.