. 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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