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

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.

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Parker 1 week 2021-09-15T00:43:13+00:00 2 Answers 0 views 0

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    0
    2021-09-15T00:44:49+00:00

    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°

    PLZ MARK AS BRAINLIST

    0
    2021-09-15T00:44:52+00:00

    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}  }

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