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Sagot :

Geometry - Isosceles Trapezoid

4. If m∠A = 70, what is m∠B?

m∠B = [tex]\color{red}{70}[/tex]

5 If m∠D=105, what is m∠B?

m∠B = [tex]\color{red}{75}[/tex]

6. If m∠B = 2x-6 and m∠A = 82, what is x?

Finding x:

[tex]2x - 6 + 82 = 180[/tex]

[tex]2x + 76 = 180[/tex]

[tex]2x = 180 - 76[/tex]

[tex] \frac{2x}{2} = \frac{104}{2} [/tex]

[tex]\color{red}{x = 52}[/tex]

7. If m∠B = 2(y + 4) and m∠D = 116, what is y?

Finding y:

[tex]2y + 4 + 116 = 180[/tex]

[tex]2y + 120 = 180[/tex]

[tex]2y = 180 - 120[/tex]

[tex] \frac{2y}{2} = \frac{60}{2} [/tex]

[tex]\color{red}{y = 30}[/tex]

8. If AC = 56cm, what is DB?

DB = [tex]\color{red}{56cm}[/tex]

9. If AC = 2x + 10 and DB = 4x-6, what is AC?

Finding x:

[tex]2x + 10 = 4x - 6[/tex]

[tex]2x - 4x = - 6 - 10[/tex]

[tex] \frac{ - 2x}{ - 2} = \frac{ - 16}{ - 2} [/tex]

[tex]x = 8[/tex]

Finding AC:

[tex]2(8) + 10[/tex]

[tex]16 + 10[/tex]

[tex]\color{red}{= 26}[/tex]

What are the properties of an Isosceles Trapezoid?

  • The legs are congruent
  • The lower and upper base angles are congruent
  • Any lower base angle is supplementary to any upper base angle
  • The diagonals are congruent

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