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The combined angle measure is 70^. The two given angles are 45^ and f^.

Mathematics

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Answer

B

Step-by-step solution

13 steps

Here are the solutions to the problems:

3.
The combined angle measure is 70∘70^\circ. The two given angles are 45∘45^\circ and f∘f^\circ.

  1. Set up the equation based on the sum of the angles.

    45∘+f∘=70∘45^\circ + f^\circ = 70^\circ
  2. Solve for ff.

    f∘=70∘−45∘f^\circ = 70^\circ - 45^\circ f∘=25∘f^\circ = 25^\circ

    The value of ff is 25\boxed{\text{25}}.

    4.
    The combined angle measure is 115∘115^\circ. The two given angles are t∘t^\circ and 90∘90^\circ (indicated by the right angle symbol).

  3. Set up the equation based on the sum of the angles.

    t∘+90∘=115∘t^\circ + 90^\circ = 115^\circ
  4. Solve for tt.

    t∘=115∘−90∘t^\circ = 115^\circ - 90^\circ t∘=25∘t^\circ = 25^\circ

    The value of tt is 25\boxed{\text{25}}.

    5.
    The combined angle measure is 180∘180^\circ (a straight angle). The two given angles are x∘x^\circ and 150∘150^\circ.

  5. Set up the equation based on the sum of the angles.

    x∘+150∘=180∘x^\circ + 150^\circ = 180^\circ
  6. Solve for xx.

    x∘=180∘−150∘x^\circ = 180^\circ - 150^\circ x∘=30∘x^\circ = 30^\circ

    The value of xx is 30\boxed{\text{30}}.

    6.
    The two given angles, 35∘35^\circ and r∘r^\circ, form a right angle, which measures 90∘90^\circ.

  7. Set up the equation based on the sum of the angles.

    35∘+r∘=90∘35^\circ + r^\circ = 90^\circ
  8. Solve for rr.

    r∘=90∘−35∘r^\circ = 90^\circ - 35^\circ r∘=55∘r^\circ = 55^\circ

    The value of rr is 55\boxed{\text{55}}.

    7. Problem Solving

  9. Determine the angle between each number on a clock face.

    A full circle is 360∘360^\circ, and there are 12 numbers on a clock.
    Angle per number = 360∘12=30∘\frac{360^\circ}{12} = 30^\circ.

  10. Identify the positions of the line and the minute hand.

    The line is drawn to the number 12. The minute hand is on 2.

  11. Calculate the angle between the line at 12 and the minute hand at 2.

    The minute hand moves 2 positions from 12 (from 12 to 1, and from 1 to 2).
    Angle = 2×30∘=60∘2 \times 30^\circ = 60^\circ.
    The angle is 60∘\boxed{\text{60}^\circ}.

    8. Test Practice
    The combined angle measure is 120∘120^\circ. The two given angles are n∘n^\circ and 80∘80^\circ.

  12. Set up the equation based on the sum of the angles.

    n∘+80∘=120∘n^\circ + 80^\circ = 120^\circ
  13. Solve for nn.

    n∘=120∘−80∘n^\circ = 120^\circ - 80^\circ n∘=40∘n^\circ = 40^\circ

    The value of nn is 40.
    Comparing this to the given options:
    A) 45
    B) 40
    C) 35
    D) 30
    The correct option is B).

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