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In parallelogram ABCD if angle A equals 5x plus 30 and angle D equals x find angle c?
In parallelogram ABCD, angle A and angle D are adjacent or consecutive angles and are supplementary, meaning the sum of their measures is equal to 180 degrees. Angles A and C are opposite angles and have the same measure. These are some important properties of parallelograms.
So to find the measure of angle C, you first have to find the measure of angle A. You can do that with a little algebra. First, set the expressions for the measures of angles A and D equal to 180 and solve for x. Then plug that value for x into the expression for the measure of angle A, which is the same as the measure for angle C.
5x + 30 + x = 180
6x + 30 = 180
6x = 150
x = 25
Therefore, 5x + 30 = 5(25) + 30 = 125 + 30 = 155
The measure of angle C is 155.
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