The opposite angles of a parallelogram are (3x-2)^0 and (x+48)^0 find the measure of each angle of the parallelogram
Answers
Hola Mate!
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Question: The opposite angles of a parallelogram are (3x-2)^0 and (x+48)^0 find the measure of each angle of the parallelogram.
(Based on lesson Quadrilaterals Grade 9)
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Answer
In a parallelogram, opposite angles are equal.
Therefore,
(3x - 2) = (x + 48) (∵opposite angles of parallelograms are equal)
3x - 2 = x + 48
3x - x = 48 + 2
2x = 50
x = 50/2
x = 25°
∴ (3x - 2)
(3(25) - 2)
(75 - 2)
∠A = 73°
∴ (x + 48)
(25 + 48)
∠C = 73°
(you must get ∠A = ∠C as opposite angles of parallelograms are equal, that is why in this answer, we have gotten equal answers)
We know that in a parallelogram, opposite sides are parallel
∴ ∠A + ∠B = 180° (co-interior angles) or (adjacent angles of a ║gms)
73° + ∠B = 180°
∠B = 180° - 73°
∠B = 107°
∠B = ∠C (opposite angles of a parallelogram are equal)
∴ ∠B = ∠C = 107°
Now the angles of the Parallelogram are as follows.
∠A = 73°
∠B = 107°
∠C = 73°
∠D = 107°
To confirm the answer, you can add all the found angles, and the must add up to 360°. Lets try it out. (NOT needed to be done in HW or exam, just for self clarification)
∠A + ∠B + ∠C + ∠D
73° + 107° + 73° + 107°
360°
∴Our answer is correct.
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Hope it Helps!
#AimBrainly
Answer:
In a parallelogram, opposite angles are equal
Therefore, (3x-2)° =(X+48)° (Since, Opposite angles of parallelogram are equal)
3x-2=X+48
3x-x=48+2
2x=50
X=50/2
X=25°
Therefore, (3x-2)
(3(25)-2)
(75-2)
<A=73°
(X+48)
(25+48)
<C=73°
<A+<B=180 (Co- interior angles) or (adjacent angles a||GMs)
73°<B=180°
<B=180°-73°
<B=107°
<B=<C (opposite angles of a parallelogram are equal)
<B=<C=107°
The angles of the parallelogram are
<A=73°
<B=107°
<C=73°
<D=107°