Step-by-step explanation:
1. Given angles are,
40°, 3x+8° , 10x+42°
Therefore, by the problem,
=> 40° + 3x+8° + 10x+42° = 180° [Angle sum property of triangle]
=> 3x + 10x = 180° - (40°+42°+8°)
=> 13x = 180° - 90°
=> 13x = 90°
[tex] = > x = \frac{90}{13} [/tex]
Hence required value of x is (90/13)°
2. Given,
12x - 18° = 5x +19° [Alternate angles]
=> 12x - 5x = 19 + 18
=> 7x = 37
[tex] = > x = \frac{37}{7} [/tex]
Hence required value of x is (37/7)°
3. Given,
Exterior angle 132°
So it's paired interior angle will be = 180° - 132° (linear pair) = 48°
Hence the angles we get are = 42° , 87° , 20x - 10°
Therefore, by the problem,
48° + 87° + 20x - 10° = 180° [Angle sum property of triangle]
=> 20x = 180 - 48 - 87 + 10
=> 20x = 55
[tex] = > x = \frac{55}{20} [/tex]
=> x = 2.75
Hence required value of x is 2.75
