Refer to the figure below to complete the following problem.
The figure is parallelogram ABCD, which is a rhombus.
If the measure of Angle B is equal to 5x - 7 and the measure of Angle D is equal to 3x + 11, then what is the measure of Angle D?
A. 9 degrees
B. 17 degrees
C. 38 degrees
D. 77 degrees
A+D = 180°
So solve that for x, and you can then determine D.
To find the measure of Angle D, we need to set up an equation using the given information.
According to the problem, the measure of angle B is equal to 5x - 7, and the measure of angle D is equal to 3x + 11.
Since a rhombus has opposite angles that are equal, we can write an equation:
Angle B = Angle D
This gives us:
5x - 7 = 3x + 11
Now, let's solve the equation for x:
5x - 3x = 11 + 7
2x = 18
Dividing both sides by 2:
x = 9
Now that we have the value of x, we can substitute it back into the equation to find the measure of angle D:
Angle D = 3x + 11
Angle D = 3(9) + 11
Angle D = 27 + 11
Angle D = 38 degrees
Therefore, the measure of Angle D is 38 degrees. The correct answer is option C.
To find the measure of angle D, we need to set up an equation using the given information.
In a parallelogram, opposite angles are congruent, which means that angle B is equal to angle D.
Given that angle B is equal to 5x - 7 and angle D is equal to 3x + 11, we can set up an equation:
5x - 7 = 3x + 11
To solve for x, we need to isolate the x term:
5x - 3x = 11 + 7
2x = 18
Divide both sides of the equation by 2 to solve for x:
x = 9
Now that we have the value of x, we can substitute it back into the equation to find the measure of angle D:
Angle D = 3x + 11 = 3(9) + 11 = 27 + 11 = 38 degrees
Therefore, the measure of angle D is 38 degrees.
The correct answer is C. 38 degrees.
I take the measure of Angle B and the measure of Angle D, and place the equal sign in between the two angles:
m∠B = m∠D
5x - 7 = 3x + 11
Then, I add 7 to the measure of angle B and the measure of angle D on both sides:
m∠B + 7 = m∠D + 7
5x - 7 + 7 = 3x + 11 + 7
Now, I can simplify. Since negative 7 and positive 7 equal 0, they cancel out:
5x = 3x + 18
Next, I subtract 3x to both sides of the simpified equation:
5x - 3x = 3x + 18 - 3x
After that, I simpify the equation the second time. Which will be simpified to:
2x = 18
Finally, I divide 2x and 18 by 2 and simpify.
2x/2 = 18/2
Since 2 divided by 2 equals 1, it will equal:
x = 18/2
After the equation is simpified, the answer would equal to:
x = 9
The equation would be:
m∠D = 3x + 11 = 3(9) + 11 = 38°
The answer is 38°.