The measure of one angle in a triangle is 2X degrees. The second angle is 3X plus 10° and the third angle is 4X −19°. Find the value of x and the measures of all three angles

Answer 1

Since the sum of the angles in a triangle is always 180°, we can set up the equation:

2X + (3X + 10°) + (4X - 19°) = 180°

Combining like terms, we get:

9X - 9° = 180°

Adding 9° to both sides, we have:

9X = 189°

Dividing both sides by 9, we find:

X = 21°

Substituting this value back into the equations for each angle, we get:

First angle: 2X = 2 * 21° = 42°
Second angle: 3X + 10° = 3 * 21° + 10° = 73°
Third angle: 4X - 19° = 4 * 21° - 19° = 79°

So, the value of X is 21°, and the measures of the three angles are 42°, 73°, and 79°.