Question

one angle of a triangle is equal to sum of other two angles. if the ratio between other two angles is 4 : 5. find all the angles?​

Answer 1

$\bf\huge\underline\blue{Answer}$

Given:

Ratio between two other angles is 4:5.

Let x be the common multiple of the ratio.

So, angle a = 4x

angle b = 5x

angle c = a + b = 4x + 5x = 9x $\bf\underbrace{one\: angle\: of \:a\:triangle \:is\: equal\: to\: sum \:of \:other\: two \:angles}$

4x + 5x + 9x = 180$\bf\underbrace {sum\:of\:all \:angles \:of \:a\:triangle \:is\:180°}$

9x + 9x = 180

18x = 180

x = $\bf\huge\frac{180}{18}$

x = 10

Substitute the values of x in the angles.

Angle a = 4x = 4 × 10 = 40°

Angle b = 5x = 5 × 10 = 50°

Angle c = 9x = 9 × 10 = 90°

$\bf\huge\boxed{Verification}$

According to the property of sum of all angles of a triangle is 180°,

angle a + angle b + angle c = 180°

40 + 50 + 90 = 180

90 + 90 = 180

180 = 180

$\bf\huge\boxed{LHS = RHS}$

Hence, verified.