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Alexxx [7]
2 years ago
15

Find the value of x, if C is on line AE

Mathematics
2 answers:
murzikaleks [220]2 years ago
3 0

Answer:

x = 11°

Step-by-step explanation:

<u>Linear Pair</u>

Two angles adjacent to each other that form a straight line.

The sum of angles of a linear pair is always equal to 180°.

⇒ m∠C = 180° - 33° = 147°

<u>Alternate Interior Angle Theorem</u>

When two parallel lines are cut by a transversal, the alternate interior angles are congruent.

From inspection of the diagram, we can see that AB ║ DC.

Therefore, AE is the transversal.

So m∠A = 33°

<u>Sum of interior angles of a triangle is 180°</u>

Therefore, the top angle of the triangle = 180° - m∠A - 2x

                                                                  = 180° - 33° - 2x              

                                                                   = 147° - 2x

<u>Angles around a point add up to 360°</u>

⇒ 33° + m∠C + 5x + (147° - 2x) = 360°

⇒ 33° + 147° + 5x + 147° - 2x = 360°

⇒ 327° + 3x = 360°

⇒ 3x = 33°

⇒ x = 11°

guapka [62]2 years ago
3 0

Answer:

x = 11°

Explanation:

  • m∠C = m∠A = 33°
  • m∠B = 2(x)
  • m∠I = 180° - 5(x)

============                       [ total interior angle in a triangle is 180° ]

<u>solve for x</u>

  • 33° + 2(x) + 180° - 5(x) = 180°
  • -3(x) = 180° - 213°
  • -3(x) = -33°
  • x = 11°
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4 0
2 years ago
Please help with this and explain how to do it, I'll give 15 points
MrRissso [65]

Answer:

Option (4).

Step-by-step explanation:

Outer diameter of the hollow metallic ball = 10 centimeters

Outer radius of this ball = \frac{10}{2} = 5 cm

Volume of the outer ball V_{1} = \frac{4}{3}\pi (r)^3

                                         = \frac{4}{3}\pi (5)^3

Inner radius of the hollow metallic ball = (5 - 1) = 4 cm

Volume of the inner hollow ball V_{2} = \frac{4}{3}\pi (4)^3

Volume of the metal used in the metallic ball = V_{1}-V_{2}

                                                                           = \frac{4}{3}\pi (5)^3-\frac{4}{3}\pi (4)^{3}

                                                                           = \frac{4}{3}\pi [(5)^3-(4)^3]

Therefore, expression given in option (4) will be used to measure the volume of the hollow metallic ball.

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The angles of two pentagons are all equal to 108°. The length of one side of each pentagon measures 11 cm.
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3 years ago
Which function represents g(x), a reflection of f(x) = 4across the x-axis?
fiasKO [112]

Answer:

Option C g(x) = -4

Step-by-step explanation:

In the question a function f(x) =4 is given and we are required to tell the reflection g(x) of the given function.

The rule of reflection for a function says that:

f(x) -> - f(x)

So, in our case the value of function is f(x) = 4, after reflection the value across the x-axis the value will become negative i.e -4,

so the required function g(x) = - 4

Hence Option C g(x) = -4 is correct option.

3 0
2 years ago
Read 2 more answers
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