Question

An exterior angle of a triangle is 110° and its two interior opposite angles are in the ratio 1 : 4. Find all the angles.

Answer 1

Hey Pretty Stranger!

Let ABC be an triangle whose side BC is Produced to form an exterior angle ACD such that ext. angle ACD = 110°

Let the interior angles be x and 4x

By exterior angle theorem, we've :

$\sf \: ext. \angle \: ACD = \angle B + \angle \: A$

$\sf \longrightarrow {110}^{ \circ} = x + 4x$

$\sf \longrightarrow {110}^{ \circ} =5x$

$\sf \longrightarrow \: x = \cancel\dfrac{110}{5}$

$\sf \longrightarrow \: x = {22}^{ \circ}$

$\dag \sf \: First \: Angle = \boxed{ \sf {22}^{ \circ} }$

$\dag \sf \: Second \: Angle = {22} \times 4 = \boxed{ \sf {88}^{ \circ} }$

$\dag \sf \: Third\: Angle = 180 -(22 + 88) = \boxed{ \sf \: {70}^{ \circ} }$

Answer 2

exterior angle = 110°

let the two interior opp. angles be 1x and 4x

the interior angle joined with 110° is 70°

sum of all interior angle is 180°

1x + 4x + 70°=180°

x = 14°

first angle is 70°

second angle 1x = 14°

third angle 4x = 56°

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