Find the mass. Volume=2.3cm cubed Density=4.1g/cm cubed
1 answer:
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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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Step-by-step explanation:
Complete the proof of the Pythagorean theorem is given below.
Statement Reason
1. ΔABC is a right triangle, with a 1. Given
right angle at ∠C
2. Draw an altitude from point C 2. From a point not on a line, exactly
to AB one perpendicular can be drawn through the point to the line
3. ∠CDB and ∠CDA are right 3. Definition of altitude
angles
4. ∠BCA ≅ ∠BDC 4. All right angles are congruent
5. ∠B ≅ ∠B 5.
6. ΔCBA ~ ΔDBC 6. AA Similarity Postulate
7. 7.
8. 8.
9. ∠CDA ≅ ∠BCA 9.
10. ∠A ≅ ∠A 10.
11. ΔCBA ~ ΔDBA 11. AA Similarity Postulate
12. 12.
13. 13.
14. 14.
15. 15. Distributive Property
16. 16.
17. 18.