if one angle of triangle is 15 degree more than its second angle.the third angle is 25 degree more than double the second angle . find the three angles of the triangle.
Answers
Answer:
2nd angle = x°
1st angle = (15 + x)°
3rd angle = (25 + 2x)°
x + (15 + x) + (25 + 2x) = 180 (Angle sum property of triangle)
x + 15 + x + 25 + 2x = 180
x + x + 2x + 15 + 25 = 180
4x + 40 = 180
4x = 180 - 40
4x = 140
x = 140 ÷ 4
x = 35
∴ 1st angle = (15 + x)°
= (15 + 35)°
= 50°
2nd angle = x°
= 35°
3rd angle = (25 + 2x)°
= (25 + 2 × 35)°
= (25 + 70)°
= 95°
Answer:
The angles are 35°, 50° and 95°
Step-by-step explanation:
Let second angle be x°.
Thus, first angle = (x + 15)°
And third angle = (2x + 25)°
Now, by ASP (Angle Sum Property) of triangle, sum of all angles is 180°.
x° + (x + 15)° + (2x + 25)° = 180°
=> x + x + 2x + 15 + 25 = 180°
=> 4x + 40 = 180°
=> x + 10 = 45° (Dividing by 4)
∴ x = 45 - 10 => 35°
∴ x + 15 = 35 + 15 => 50°
∴ 2x + 25 = 2(35) + 25 = 70 + 25 => 95°
Thus, the angles are 35°, 50° and 95°