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The sum of angle on a straight line is

Mathematics

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Answer

D

180∘180^\circ

Step-by-step solution

4 steps

Here are the solutions to the questions:

  1. The sum of angle on a straight line is A straight line measures 180∘180^\circ. The correct option is (d) 180∘180^\circ.

  2. The triangle which has its three sides equal is A triangle with three equal sides is called an equilateral triangle. The correct option is (a) Equilateral.

  3. Using Pythagoras theorem, solve for b.

  1. Apply the Pythagorean theorem a2+b2=c2a^2 + b^2 = c^2, where a=6a=6 and c=10c=10 (hypotenuse).

    $$
    6^2 + b^2 = 10^2
    $$
    
  2. Calculate the squares.

    $$
    36 + b^2 = 100
    $$
    
  3. Isolate b2b^2.

    $$
    b^2 = 100 - 36
    $$
    $$
    b^2 = 64
    $$
    
  4. Take the square root to find bb.

    $$
    b = \sqrt{64}
    $$
    $$
    b = 8
    $$
    The correct option is **(a) b=8**.
    

    4. The sum of the three angles in a triangle is The sum of the interior angles of any triangle is always 180∘180^\circ. The correct option is (d) 180∘180^\circ.

    1. Angle x and y are called ____ angles Angles x and y are on opposite sides of the transversal and between the two parallel lines. They are called alternate interior angles. The correct option is (b) alternate.

    2. Sine 30∘30^\circ, cos 30∘30^\circ, tan 30∘30^\circ

      • sin⁡30∘=12\sin 30^\circ = \boxed{\frac{1}{2}}
      • cos⁡30∘=32\cos 30^\circ = \boxed{\frac{\sqrt{3}}{2}}
      • tan⁡30∘=13 or 33\tan 30^\circ = \boxed{\frac{1}{\sqrt{3}} \text{ or } \frac{\sqrt{3}}{3}}
    3. sin 60∘60^\circ, cos 60∘60^\circ, tan 60∘60^\circ

      • sin⁡60∘=32\sin 60^\circ = \boxed{\frac{\sqrt{3}}{2}}
      • cos⁡60∘=12\cos 60^\circ = \boxed{\frac{1}{2}}
      • tan⁡60∘=3\tan 60^\circ = \boxed{\sqrt{3}}
    4. sin 45∘45^\circ, cos 45∘45^\circ, tan 45∘45^\circ

      • sin⁡45∘=12 or 22\sin 45^\circ = \boxed{\frac{1}{\sqrt{2}} \text{ or } \frac{\sqrt{2}}{2}}
      • cos⁡45∘=12 or 22\cos 45^\circ = \boxed{\frac{1}{\sqrt{2}} \text{ or } \frac{\sqrt{2}}{2}}
      • tan⁡45∘=1\tan 45^\circ = \boxed{1}
    5. The sum of angle at a point is The sum of angles around a central point is 360∘360^\circ. The answer is 360∘\boxed{360^\circ}.

    6. Write short notes on the followings

      • a) Acute angle: An angle that measures less than 90∘90^\circ.
      • b) Obtuse angle: An angle that measures greater than 90∘90^\circ but less than 180∘180^\circ.
      • c) Reflex angle: An angle that measures greater than 180∘180^\circ but less than 360∘360^\circ.
      • d) Right angle triangle: A triangle that contains one angle exactly equal to 90∘90^\circ.
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