Answer:
m∠A = 91°
m∠B = 146°
m∠C = 89°
m∠D = 34°
Step-by-step explanation:
- If the four vertices of a quadrilateral lie on the edge of a circle, then this quadrilateral is called cyclic quadrilateral
- In the cyclic quadrilateral each two opposite angles are supplementary (means the sum of their measures is 180°)
- The sum of the measures of the interior angles of any quadrilateral is 360°
In quadrilateral ABCD
∵ A, B, C, And D lie on the circumference of the circle
∴ ABCD is a cyclic quadrilateral
∴ The sum of the measures of each opposite angles is 180°
∵ ∠A and ∠C are opposite angle in the cyclic quadrilateral ABCD
∴ m∠A + m∠C = 180°
∵ m∠A = (2x + 3)°
∵ m∠C = (2x + 1)°
- Add them and equate the answer by 180
∴ (2x + 3) + (2x + 1) = 180
- Add the like terms in the left hand side
∴ 4x + 4 = 180
- Subtract 4 from both sides
∴ 4x = 176
- Divide both sides by 4
∴ x = 44
Substitute the value of x in the expressions of angle A, C, D
∵ m∠A = 2(44) + 3 = 88 + 3
∴ m∠A = 91°
∵ m∠C = 2(44) + 1 = 88 + 1
∴ m∠C = 89°
∵ m∠D = x - 10
∴ m∠D = 44 - 10
∴ m∠D = 34°
- ∠B and ∠D are opposite angles in the cyclic quadrilateral ABCD
∴ m∠B + m∠D = 180°
∴ m∠B + 34 = 180
- Subtract 34 from both sides
∴ m∠B = 146°
10x454x0.55=2,497 grams of fruit
<span>216:270 = 4:5
divide top and bottom by 54
hope it helps</span>
From my research, the original system of equations contain the following equations:
<span>2x − y = −4
3x + 5y = 59
where obtained solution is x = 3
Among the choices, it is easier to substitute </span><span>3x + 5y = 59 with one of the choices to see if they yield the same solution set. From trial-and-error, the equation that can replace the original equation is " 13x = 39 ". Among the choices, it is the 4th choice.</span>
<span>7.158 x 10^9 rounds to 7 x 10^9
</span>7 x 10^9 means 7 followed by 9 zeros.
7.158 * 10^9 is approximately equal to 7 * 10^9 = 7,000,000,000
