Answer:
Concept:
Here, we need to know about the idea of a cyclic quadrilateral.
In a <u>cyclic quadrilateral</u>, the sum of either pair of opposite angles is supplementary, which means they add up to 180°.
Please refer to the attachment below for a graphical explanation
Solve:
<u>Given information</u>
∠DAB = 2x + 4
∠ABC = 4y + 4
∠BCD = 4x + 2
∠CDA = 3y + 8
<u>Derived formula from the concept</u>
∠DAB + ∠BCD = 180°
∠ABC + ∠CDA = 180° (Not Important)
<u>Substitute values into the formula that includes ∠DAB</u>
∠DAB + ∠BCD = 180°
(2x + 4) + (4x + 2) = 180
<u>Combine like terms</u>
2x + 4 + 4x + 2 = 180
2x + 4x + 4 + 2 = 180
6x + 6 = 180
<u>Subtract 6 on both sides</u>
6x + 6 - 6 = 180 - 6
6x = 174
<u />
<u>Divide 6 on both sides</u>
6x / 6 = 174 / 6
x = 29
<u>Substitute values into the angle expression of ∠DAB</u>
∠DAB = 2x + 4
∠DAB = 2 (29) + 4
∠DAB = 58 + 4
Hope this helps!! :)
Please let me know if you have any questions
