Question

Two angles are in the ratio 4: 7. On increasing the first angle by 100${}^{\circ }$ the ratio changes to 2:1. Find the value of the second angle.

• A. 70${}^{\circ }$
• B. 40${}^{\circ }$
• C. 140${}^{\circ }$
• D. 10${}^{\circ }$

Answer 1

The correct option is A

70${}^{\circ }$

Given: The ratio of angles initially = 4: 7

$\therefore$ Let the angles be 4$x$ and 7$x$.

Increasing the first angle by 100${}^{\circ }$, we get

$\Rightarrow$ 4$x$ + 100${}^{\circ }$

Now the ratio is 2:1

$\therefore$ Now let the angles be 2$y$ and $y$

$\Rightarrow$ $y$ = 7$x$-------(1) ($\because$ Both are the values of the second angle)

and 2$y$ = 4$x$ + 100${}^{\circ }$-------(2) ($\because$ Both are the values of the first angle)

Now substituting the value of $y$ in (2) we get

14$x$ = 4$x$ + 100${}^{\circ }$

$\Rightarrow$ 10$x$ = 100${}^{\circ }$

$\Rightarrow$ $x$ = 10${}^{\circ }$

$\therefore$ The value of thre second angle = 7$x$

= 70${}^{\circ }$