Question

the angel of quadrilateral are (5x) degree, (3x+10)degree, (6x-20), (x+25) degree find the value of x and measure of each angle of the quadrilateral​

Answer 1

$\LARGE\star\mathfrak{\underline{\underline{\red{answer: }}}}$

$\sf{given : } \\ \sf{angle \: 1 = 5x \degree} \\ \sf{angle \: 2 = 3x + 10 \degree} \\ \sf{angle \: 3= 6x - 20 \degree} \\ \sf{angle \: 4 = x + 25 \degree}$

$\sf{by \: angle \: sum \: property \: of \: a \: quadrilateral : } \\ \sf{angle \: 1 + angle \: 2 + angle \: 3 + angle \: 4 = 360 \degree } \\ \sf{(5x) +( 3x + 10 )+ (6x - 20) + (x + 25 )= 360 \degree} \\ \sf{15x + 15 = 360 \degree} \\ \sf{15x = 360 - 15 \degree} \\ \sf{15x = 345} \\ \sf{x = \frac{345}{15} } \\ \boxed{ \sf{x = 23}}$

$\boxed{ \sf{angle \: 1 = 5x = 5(23) = 115 \degree}} \\ \boxed{ \sf{angle \: 2 = 3x + 10 = 79 \degree}} \\ \boxed{ \sf{angle \: 3 = 6x - 20 = 6(23) - 20 = 118 \degree}} \\ {\boxed{ \sf{angle \: 4 =x + 25 = (23) + 25 = 48 \degree}}}$