In parallelogram ABCD, angle B is 5 times as large as angle C. What is the measure in degrees of angle B?
A. 60
B. 100
C. 120
D. 150
Its so confusing to me
I know that a parallelogram adds up 180 but this is looking for one angle so obviously you would add that by itself and add it with 5 divided by that and then repeat the previous step.
The sum of the angles of all four-sided figures, including parallelograms is 360 degrees.
I chose D by the way
Read carefully.
https://www.google.com/search?ei=4LNMXaiXM8zYsQXM36yQBg&q=parallelogram+interior+angles+sum&oq=parallelogram+interior+angles&gs_l=psy-ab.1.3.0i71l8.0.0..6197...0.0..0.0.0.......0......gws-wiz.h0qCkuyKcKo
150
Wait but I thought parallelograms all equal 180 even when you search it up on google it says it 🤔
In a parallogram, the sum of 2 adjacent angles is 180°.
so,
x + 5x = 180
x = ....
so the larger is 5x or .....
150
okay
To find the measure of angle B in parallelogram ABCD, you can use the fact that opposite angles in a parallelogram are congruent. In other words, angle B and angle D of the parallelogram are equal.
Let's assume the measure of angle C is x degrees. Since angle B is five times as large as angle C, angle B can be represented as 5x degrees.
Since angle B and angle D are congruent, angle D can also be represented as 5x degrees.
Since the sum of the angle measures in a parallelogram is 360 degrees, we can set up an equation: angle B + angle C + angle D + angle A = 360.
Substituting the values we know, the equation becomes: 5x + x + 5x + x = 360.
Combining like terms, the equation simplifies to: 12x = 360.
Dividing both sides of the equation by 12, we find that x = 30.
Now we can find the measure of angle B by substituting x back into the equation: angle B = 5x = 5 * 30 = 150 degrees.
Therefore, the correct answer is D. 150 degrees.