Answer:
x = 8 degree
Step-by-step explanation:
8x - 4 = 60 degree (being alternate interior angle)
8x = 60 + 4
8x = 64
x = 64/8
x = 8 degree
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°
Answer:
An irregular polygon is any polygon that is not a regular polygon. It can have sides of any length and each interior angle can be any measure. They can be convex or concave, but all concave polygons are irregular since the interior angles cannot all be the same.
Step-by-step explanation:
Answer:
C) 
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The probability that Mae will roll an odd number
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Step-by-step explanation:
<u><em>Step(i):-</em></u>
<em>Given that Mae has a number cube with 6 sides that are numbered 1 through 6.</em>
<em>n(S) = { 1,2,3,4,5,6,} = 6</em>
<em>Let 'E ' be the event of odd numbers</em>
<em>Mae will roll an odd number</em>
<em>n(E) = {1, 3, 5} = 3</em>
<u>Step(ii):-</u>
<u>The probability that Mae will roll an odd number</u>
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Answer:
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Step-by-step explanation:
