Which of the following quadrilaterals have diagonals that bisect each other?
1 answer:
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Factor each of the following differences of two squares and write your answer together with solution.
Rewrite . The difference of squares can be factored using the rule:
.
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<h3><u>2. 49 - x²</u></h3>Rewrite 49-x² as 7²-x². The difference of squares can be factored using the rule: .
Reorder the terms.
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<h3><u>3. 81 - c²</u></h3>Rewrite 81-c²as 9²-c². The difference of squares can be factored using the rule: .
Reorder the terms.
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<h3><u>4</u><u>.</u><u> </u><u>m²</u><u>n</u><u>²</u><u> </u><u>-</u><u> </u><u>1</u></h3>Rewrite m²n² - 1 as . The difference of squares can be factored using the rule:
.
The value of x is 81
Step-by-step explanation:
The sum of the interior angles of any quadrilateral is 360°
- The measure of ∠1 is 40% of the sum of the angle measures of the quadrilateral
- The measure of ∠2 is 12.5% of the sum of the angle measures of the quadrilateral
- The measure of ∠3 is 25% of the sum of the angle measures of the quadrilateral
- We need to find the value of x
∵ The figure have 4 sides
∴ The figure is a quadrilateral
∵ The sum of the measures of the interior angles of a
quadrilateral is 360°
- Add the four angles and equate the sum by 360
∴ m∠1 + m∠2 + m∠3 + x = 360
∵ m∠1 = 40% of the sum of the angle measures of the quadrilateral
∴ m∠1 = 40% × 360 = × 360 = 144°
∵ m∠2 = 12.5% of the sum of the angle measures of the quadrilateral
∴ m∠2 = 12.5% × 360 = × 360 = 45°
∵ m∠3 = 25% of the sum of the angle measures of the quadrilateral
∴ m∠3 = 25% × 360 = × 360 = 90°
- Substitute these values in the equation above
∴ 144 + 45 + 90 + x = 360
- Add the like terms in the left hand side
∴ 279 + x = 360
- Subtract 279 from both sides
∴ x = 81°
The value of x is 81
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You can learn more about the polygons in brainly.com/question/6281564
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