Question

Two angles of a triangle are in the ratio 7: 11 and the third angle is 72. Find the two angles,​

Answer 1

Answer:

42,66

Step-by-step explanation:

sum of all angles =180

7x +11x+72=180

18x=108

x=108/18

x=6

7x=7×6

=42

11x=11×6

=66

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Answer 2

Given :

• Two angles of a triangle are in the ratio 7:11 .
• Third angle of triangle is 72° .

To Find :

• Two angles .

Solution :

$\longmapsto\tt{Let\:first\:angle\:be=7x}$

$\longmapsto\tt{Let\:second\:angle\:be=11x}$

As we know that Sum of all angles of a triangle is 180° . So ,

$\longmapsto\tt{7x+11x+72^{\circ}=180^{\circ}}$

$\longmapsto\tt{18x+72^{\circ}=180^{\circ}}$

$\longmapsto\tt{18x=180^{\circ}-72^{\circ}}$

$\longmapsto\tt{18x=108^{\circ}}$

$\longmapsto\tt{x=\cancel\dfrac{108}{18}}$

$\longmapsto\tt\bf{x=6}$

Value of x is 6 ..

Therefore :

$\longmapsto\tt{Measure\:of\:First\:Angle=7(6)}$

$\longmapsto\tt\bf{42^{\circ}}$

$\longmapsto\tt{Measure\:of\:First\:Angle=11(6)}$

$\longmapsto\tt\bf{66^{\circ}}$

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VERIFICATION :

$\longmapsto\tt{7x+11x+72^{\circ}=180^{\circ}}$

$\longmapsto\tt{7(6)+11(6)+72^{\circ}=180^{\circ}}$

$\longmapsto\tt{42^{\circ}+66^{\circ}+72^{\circ}=180^{\circ}}$

$\longmapsto\tt\bf{180^{\circ}=180^{\circ}}$

HENCE VERIFIED