Answer:
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°
