. The opposite angles of a parallelogram are
are (3x - 2) and (x + 48) Find the measure of each angle of the parallelogram.
Best Answer
Explanation:
Let the parallelogram be ABCD & the angles of parallelogram be <A,<B,<C & <D
From the given question, opposite angles of a parallelogram are (3x-2) & (x+48).
Let <A=3x-2 & <B=x+48
As we know that, “the opposite angles of a parallelogram are always equal”. Therefore, we can write;
(3x-2)=(x+48)
⇒3x-x=48+2
⇒2x=50
⇒x=50/2
⇒x=25
Substituting the value of x in 3x-2, we get;
3(25)-2
=75-2
=73º
⇒<A=<C=73
Finding the measure of other two angles:
We know that, the sum of adjacent angles of a parallelogram is equal to 180.
∴ <A+<B=180º
⇒73º+<B=180º
⇒<B=180º-73º
⇒<B=107º
∴ <D=107º
Therefore, the measure of each angle of the parallelogram is <A=73º,<B=107º,<C=73º,<D=107º.
Final answer:
Hence, we measured all the angles of parallelogram as;<A=73º,<B=107º,<C=73º,<D=107º.
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