Answer:
1) m∠U = 90°
2) m∠C = 80°
Step-by-step explanation:
1) The given figure is a quadrilateral
The sum of the interior angles of quadrilateral = 360°
∴ The sum of the interior angles of the given figure = 360°
Therefore, we have;
80° + 24·x + 4 + 6 + 21·x + 90° = 360°
80° + 45·x + 10 + 90° = 360°
x = (360°- (80° + 10° + 90°))/45 = 4
x = 4
m∠U = 6 + 21·x = 6 + 21 × 4 = 90
m∠U = 90°
2) The sum of the interior angles of the given quadrilateral = 360°
∴ 21·x + 6 + 20·x + 24·x + 4 + 21·x + 6 = 360°
86·x + 16 = 360°
x = (360° - 16°)/86 = 4
x = 4
m∠C = 20·x = 20 × 4 = 80
m∠C = 80°
3) In the figure, some angles are left out, therefore, more information on the remaining angles required
Answer:
![\dfrac{40}{42}](https://tex.z-dn.net/?f=%5Cdfrac%7B40%7D%7B42%7D)
Step-by-step explanation:
Let the numerator of the fraction=x
Since the denominator of a fraction is two more than the numerator.
Denominator=x+2
The fraction is therefore:
![\dfrac{x}{x+2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7Bx%2B2%7D)
If both numerator and denominator are decreased by six, the fraction becomes:
![\dfrac{x-6}{x+2-6}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx-6%7D%7Bx%2B2-6%7D)
The simplified result is ![\dfrac{17}{18}](https://tex.z-dn.net/?f=%5Cdfrac%7B17%7D%7B18%7D)
Therefore:
![\dfrac{x-6}{x+2-6}=\dfrac{17}{18}\\$Next, we solve for x\\Cross multiply\\18(x-6)=17(x+2-6)\\18(x-6)=17(x-4)\\Expand the bracket\\18x-108=17x-68\\Collect like terms\\18x-17x=-68+108\\x=40](https://tex.z-dn.net/?f=%5Cdfrac%7Bx-6%7D%7Bx%2B2-6%7D%3D%5Cdfrac%7B17%7D%7B18%7D%5C%5C%24Next%2C%20we%20solve%20for%20x%5C%5CCross%20multiply%5C%5C18%28x-6%29%3D17%28x%2B2-6%29%5C%5C18%28x-6%29%3D17%28x-4%29%5C%5CExpand%20the%20bracket%5C%5C18x-108%3D17x-68%5C%5CCollect%20like%20terms%5C%5C18x-17x%3D-68%2B108%5C%5Cx%3D40)
Substituting x=40 into the initial fraction
![\dfrac{x}{x+2}=\dfrac{40}{40+2}=\dfrac{40}{42}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7Bx%2B2%7D%3D%5Cdfrac%7B40%7D%7B40%2B2%7D%3D%5Cdfrac%7B40%7D%7B42%7D)
Therefore, the original fraction is ![\dfrac{40}{42}](https://tex.z-dn.net/?f=%5Cdfrac%7B40%7D%7B42%7D)
Answer:
its A
Step-by-step explanation:
Hope it helps
It's 34.
You can either intuitively know 25% means one-fourth and divide 136 by 4
Or
Convert the percentage to a decimal and multiply. 136 * 0.25 = 34