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Calculate with reasons the value of b, c, d, and e. Also determine with reasons the value of unknowns x in the given diagrams.

Mathematics

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2 parts
a

x=30∘x=30^\circ

b

x=60∘x=60^\circ

Step-by-step solution

6 steps

here are the solutions for the questions visible in the image:

1b) Calculate with reasons the value of b,c,d,b, c, d, and ee.
Based on the partial calculation provided in the image:

Step 1: Calculate the value of bb.

b=130∘−80∘+40∘b = 130^\circ - 80^\circ + 40^\circ b=50∘+40∘b = 50^\circ + 40^\circ b=90∘b = 90^\circ

The value of bb is b=90∘\boxed{b=90^\circ}.
The values for c,d,c, d, and ee cannot be determined as the relevant diagram or expressions are not visible in the image.

  1. Determine with reasons the value of unknowns.

Part a· 3 steps

  1. Identify the relationship between the given angles.

    The angles x+20∘x+20^\circ and 3x−40∘3x-40^\circ are vertically opposite angles.

  2. Set up the equation based on the property of vertically opposite angles.

    Vertically opposite angles are equal.

    x+20∘=3x−40∘x+20^\circ = 3x-40^\circ

  3. Solve for xx.

    Subtract xx from both sides:

    20∘=2x−40∘20^\circ = 2x-40^\circ

    Add 40∘40^\circ to both sides:

    20∘+40∘=2x20^\circ+40^\circ = 2x 60∘=2x60^\circ = 2x

    Divide by 2:

    x=60∘2x = \frac{60^\circ}{2} x=30∘x = 30^\circ

    The value of xx is x=30∘\boxed{x=30^\circ}.

Part b

x=60∘x=60^\circ

  1. Identify the relationship between the given angles.

    The angles 120∘120^\circ and 120∘−x120^\circ-x form a linear pair (angles on a straight line).

  2. Set up the equation based on the property of angles on a straight line.

    Angles on a straight line sum to 180∘180^\circ.

    120∘+(120∘−x)=180∘120^\circ + (120^\circ-x) = 180^\circ

  3. Solve for xx.

    240∘−x=180∘240^\circ - x = 180^\circ

    Subtract 240∘240^\circ from both sides:

    −x=180∘−240∘-x = 180^\circ - 240^\circ −x=−60∘-x = -60^\circ

    Multiply by −1-1:

    x=60∘x = 60^\circ

    The value of xx is x=60∘\boxed{x=60^\circ}.

    1. Prove that AB∥CDAB \parallel CD. The diagram or any additional information required to prove that AB∥CDAB \parallel CD is not visible in the image. Please provide the full question with the diagram.
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