Question

If one of the angle of a triangle is 65° and the other two angles are in the ratio of 2:3. Find the

other two angles.​

Answer 1

Step-by-step explanation:

GIVEN THAT :-

✓ One angle of a triangle = 65 °

✓ Other two angles are in ratio of 2:3

FORMULA

• The sum of All three angles of triangle = 180°

Solution

• Let Other two angles which are in ratio of 2:3 are 2x and 3x respectively.

Now

2x + 3x + 65 ° = 180°

5x = 180° -65°

5x = 115°

x = 115°/5

x = 23°

Now the angles 2x = 2× 23 = 46°

3x = 3 × 23 = 69°

Now the other two Angles which are in ratio of 2:3 are 46° and 69° respectively ..

Answer 2

Answer:

Two angles of triangle are $46$° and $69$° .

Step-by-step explanation:

To find : two angles of triangle .

Given : one of the angle of a triangle is 65° and the other two angles are in the ratio of 2:3.  

Solution :

• As per given data we know that one of the angle of a triangle is 65° and the other two angles are in the ratio of 2:3.  
• Let , $2x$  and $3x$ be two angles in the ratio .
• We know that , according to angle sum property measure of all three angles of triangle is $180$° .
• According to angle sum property we write as ,
• $65 + 2x + 3x = 180$°
• Using transposition method we find the value of $x$ , by taking constant at RHS and leaving variable at LHS .

         $65 + 2x + 3x = 180 \\\\65 + 5x = 180 \\\\ 5x = 180 -65 \\\\5x = 115\\\\x = \frac{115}{5} \\\\x = 23$

• Now , substituting the value of $x$ in  $2x$  and $3x$ to find original measure of angles  .
• $2x = 2\times23 =46$°
• $3x = 3\times 23 = 69$°