Find the three angles of a triangle if the sum of the first angle and twice the second equals the third and, and if four times the second angle is 15 degrees more than the third.
write a system of equations, then write a matrix equation. solve the equation and write a sentence.

First Angle = 45°

Second Angle = 30°

Third Angle = 105°  

Step-by-step explanation:

First angle + 2(Second angle ) = Third Angle

4(second angle) = Third Angle + 15°

or, Third angle = 4(second angle)  - 15° ...(1)

⇒First angle + 2(Second angle )  = 4(second angle)  -  15°

or, First angle  = 2(second angle)  -  15° ... (2)

Now by ANGLE SUM PROPERTY of a triangle:

First angle+ Second angle + Third Angle  = 180°

Now, putting the values of (1) , (2) in above expression,

{2(Second angle)  -  15° } +  Second angle +{ 4(second angle)  - 15°} = 180°

is the required equation.

or, 7(Second angle) - 30° = 180°

or, 7(Second angle)  =   30° +   180°  =  210°

⇒ Second angle = 210°/ 7  = 30°

Now, First angle  = 2(second angle)  -  15°

                              = (2 x 30°)  - 15°  = 45°

and, Third angle = 4(second angle)  - 15°

                            = 4 x 30°  - 15°  =  120 - 15°  = 105°