Question

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

Answer 1

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

Answer 2

Answer:

The other angles are $30^\circ$ and $45^\circ$

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:

$2x+3x+105^\circ=180^\circ\\5x+105^\circ=180^\circ\\5x=180^\circ-105^\circ\\x=15^\circ$

Then the other angles are:

$2x=2(15)=30^\circ\\3x=3(15)=45^\circ$