Question

In a triangle the first angle is half or second,and the second is two thirds of third angle what is the value of first angle

Answer 1

Step-by-step explanation:

Let 3rd angle be x°.

So 2nd angle=2x/3° and 1st angle=4x/3°.

ATQ,4x/3+2x/3+X=180

or 4x+2x+3x/3=180

or 9x/3=180

or x=180×3/9=60

So 1st angle=4×60/3=80°

Answer 2

Question: In a triangle the first angle is half of second and the second is two thirds of third angle. what is the value of first angle?

Answer:

The value of the first angle is 30°

Step-by-step explanation:

Let the measure of 3rd angle be $x$.

According to the question,

The 2nd angle is two-thirds of the 3rd angle, i.e.,

2nd angle = $\frac{2}{3}$ of $3^{rd}$ angle

                = $\frac{2}{3}\times x$

                = $\frac{2}{3}x$

Also, 1st angle = half of the second angle

1st angle = $\frac{1}{2}$ of $\frac{2}{3}x$

               = $\frac{1}{3}x$

In a triangle,

1st angle + 2nd angle + 3rd angle = 180° (Angle sum property)

⇒ $\frac{1}{3}x+\frac{2}{3}x+x=180^0$

Simplify the equation as follows:

⇒ $\frac{x+2x+3x}{3}=180^0$

⇒ $\frac{6x}{3} =180^0$

⇒ $x=\frac{180\times 3}{6}$

⇒ $x=$ 90°

Since, the 1st angle = $\frac{1}{3}x$

Substituting the value of $x=$ 90°, we get

1st angle = $\frac{1}{3}\times 90$

               = $30^0$

Therefore, the value of the first angle is 30°.

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