in a triangle two angles are in the ratio 2:3 and third angle is 105. find the measures.

2 thoughts on “in a triangle two angles are in the ratio 2:3 and third angle is 105. find the measures.”

1. Answer:

   The other angles are [tex]30^\circ[/tex] and [tex]45^\circ[/tex]

   Step-by-step explanation:

   Let the missing angle be represented as x

   Then the two angles of ration 2:3, can be represented as 2x and 3x.

   Using the triangle-angle-sum theorem:

   [tex]2x+3x+105^\circ=180^\circ\\5x+105^\circ=180^\circ\\5x=180^\circ-105^\circ\\x=15^\circ[/tex]

   Then the other angles are:

   [tex]2x=2(15)=30^\circ\\3x=3(15)=45^\circ[/tex]

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2. Answer:

   30 and 45

   Step-by-step explanation:

   Sum of all angles of triangle is 180 degree so

   2x + 3x + 105 = 180 this gives

   5x = 75 this gives

   X= 15

   So 2x= 2(15) =30 degree

   And 3x = 3(15) = 45 degree

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