Two consecutive angles of a parallelogram have measures 4(x+5) and 2(3x+20) respectively. Find the measures of the angles

Any "two consecutive" angles of a parallelogram must be supplementary.

so

4(x+5) + 2(3x+20) = 180
4x + 20 + 6x + 40 = 180
10x = 120
x = 12

so sub that back into the originals to get
68º and 112º

In a parallelogram, opposite angles are congruent. Therefore, the given angles are consecutive and opposite angles.

Let's set up the equation to find the value of x:

4(x+5) = 2(3x+20)

First, distribute the 4 and 2:

4x + 20 = 6x + 40

Next, subtract 4x from both sides:

20 = 2x + 40

Now, subtract 40 from both sides:

-20 = 2x

Divide both sides by 2:

-10 = x

Now that we have the value of x, we can find the measures of the angles:

The first angle = 4(x+5)
Substituting x = -10:

= 4(-10+5)
= 4(-5)
= -20

The second angle = 2(3x+20)
Substituting x = -10:

= 2(3(-10)+20)
= 2(-30+20)
= 2(-10)
= -20

Both angles have a measure of -20.

To find the measures of the angles in a parallelogram, we need to use the property that opposite angles in a parallelogram are congruent.

Let's label the two consecutive angles as angle A and angle B.

We are given that the measure of angle A is 4(x + 5), and the measure of angle B is 2(3x + 20).

Since opposite angles are congruent in a parallelogram, we have the equation:

Angle A = Angle B

4(x + 5) = 2(3x + 20)

Now, let's solve for x to find the value of x:

4(x + 5) = 2(3x + 20)

Distribute the multiplication:

4x + 20 = 6x + 40

Subtract 4x from both sides of the equation:

20 = 2x + 40

Subtract 40 from both sides of the equation:

-20 = 2x

Divide both sides of the equation by 2:

-10 = x

Now that we have found the value of x, we can substitute it back into the expressions for the angles to find their measures:

Angle A = 4(x + 5) = 4(-10 + 5) = 4(-5) = -20 degrees

Angle B = 2(3x + 20) = 2(3(-10) + 20) = 2(-30 + 20) = 2(-10) = -20 degrees

Therefore, the measures of the angles in the parallelogram are both -20 degrees.