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JOAL is a parallelogram. Find the m ∠∠ = O.

JOAL is a parallelogram. Find the m ∠∠ = O.-example-1
User KOVIKO
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Since JOAL is a parallelogram, the measure of angle O is equal to 113°.

In Mathematics, a parallelogram is a type of quadrilateral and two-dimensional geometrical figure that is composed of two equal and parallel opposite sides.

According to the opposite angles theorem, the opposite angles of a parallelogram are always congruent and all the four angles add up to 360 degrees;

m∠O ≅ m∠J

m∠A ≅ m∠L

In this context, we have the following angle sum:

m∠O + m∠J + m∠A + m∠L = 360

5x - 7 + 5x - 7 + 3x - 5 + 3x - 5 = 360

16x - 24 = 360

16x = 384

x = 384/16

x = 24°

For the measure of angle O, we have;

m∠O = 5(24) - 7

m∠O = 113°

User Ensnare
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In a parallelogram, the sum of two adjacent angles is always 180°, then


(5x-7)+(3x-5)=180

Therefore


\begin{gathered} 8x-12=180 \\ \\ 8x=192 \\ \\ x=(192)/(8) \\ \\ x=24 \end{gathered}

Then the angle m∠O is


\begin{gathered} m\angle O=5x-7 \\ \\ m\operatorname{\angle}O=5\cdot24-7 \\ \\ m\operatorname{\angle}O=120-7 \\ \\ m\operatorname{\angle}O=113 \end{gathered}

Final answer:


m\operatorname{\angle}O=113

User Gabbi
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