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Class test Find value of x in each case Also provide your reason

Mathematics

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Here are the values of xx for each diagram:

1. Top Left Diagram

  1. Identify the relationship between the angles.

    The angles 60∘60^\circ and xx form a right angle.
    Reason: Angles in a right angle sum to 90∘90^\circ.

  2. Set up the equation and solve for xx.

    60∘+x=90∘60^\circ + x = 90^\circ x=90∘−60∘x = 90^\circ - 60^\circ x=30∘x = \boxed{\text{30}^\circ}

    1. Top Right Diagram

  3. Identify the relationship between the angles.

    The angles 30∘30^\circ, 80∘80^\circ, and 2x2x lie on a straight line.
    Reason: Angles on a straight line sum to 180∘180^\circ.

  4. Set up the equation and solve for xx.

    30∘+80∘+2x=180∘30^\circ + 80^\circ + 2x = 180^\circ 110∘+2x=180∘110^\circ + 2x = 180^\circ 2x=180∘−110∘2x = 180^\circ - 110^\circ 2x=70∘2x = 70^\circ x=70∘2x = \frac{70^\circ}{2} x=35∘x = \boxed{\text{35}^\circ}

    2. Middle Left Diagram

  5. Identify the relationship between the angles.

    The angles 2x2x and 26∘26^\circ form a right angle.
    Reason: Angles in a right angle sum to 90∘90^\circ.

  6. Set up the equation and solve for xx.

    2x+26∘=90∘2x + 26^\circ = 90^\circ 2x=90∘−26∘2x = 90^\circ - 26^\circ 2x=64∘2x = 64^\circ x=64∘2x = \frac{64^\circ}{2} x=32∘x = \boxed{\text{32}^\circ}

    2. Middle Right Diagram

  7. Identify the relationship between the angles.

    Assuming the horizontal line is a straight line, the angles xx and 150∘150^\circ are supplementary.
    Reason: Angles on a straight line sum to 180∘180^\circ.

  8. Set up the equation and solve for xx.

    x+150∘=180∘x + 150^\circ = 180^\circ x=180∘−150∘x = 180^\circ - 150^\circ x=30∘x = \boxed{\text{30}^\circ}

    3. Bottom Left Diagram

  9. Identify the relationship between the angles.

    The angles 22∘22^\circ, xx, and 77∘77^\circ are the interior angles of a triangle.
    Reason: Angles in a triangle sum to 180∘180^\circ.

  10. Set up the equation and solve for xx.

    22∘+x+77∘=180∘22^\circ + x + 77^\circ = 180^\circ x+99∘=180∘x + 99^\circ = 180^\circ x=180∘−99∘x = 180^\circ - 99^\circ x=81∘x = \boxed{\text{81}^\circ}

    3. Bottom Right Diagram

  11. Identify the relationship between the angles.

    The angles x2\frac{x}{2} and 74∘74^\circ are adjacent angles on a straight line.
    Reason: Angles on a straight line sum to 180∘180^\circ.

  12. Set up the equation and solve for xx.

    x2+74∘=180∘\frac{x}{2} + 74^\circ = 180^\circ x2=180∘−74∘\frac{x}{2} = 180^\circ - 74^\circ x2=106∘\frac{x}{2} = 106^\circ x=106∘×2x = 106^\circ \times 2 x=212∘x = \boxed{\text{212}^\circ}

    Last Problem (Bottom Diagram)

  13. Identify the relationship between the angles.

    The three angles, each marked as xx, lie on a straight line.
    Reason: Angles on a straight line sum to 180∘180^\circ.

  14. Set up the equation and solve for xx.

    x+x+x=180∘x + x + x = 180^\circ 3x=180∘3x = 180^\circ x=180∘3x = \frac{180^\circ}{3} x=60∘x = \boxed{\text{60}^\circ}
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