TWO ANGLES ARE ADJACENT AND FORM AND ANGLE OF 150.THE LARGER ANGLE IS 30 MORE THAN TWICE THE SMALLER.FIND THE ANGLES. CHAPTER- LINES AND ANGLES

If your measuring unit is a degree then:

THE LARGER ANGLE IS 30 MORE THAN TWICE THE SMALLER.

mean:

α = 2 β + 30°

TWO ANGLES ARE ADJACENT AND FORM AND ANGLE OF 150

mean:

α + β = 150°

Replace α = 2 β + 30° in this equation.

α + β = 150°

2 β + 30° + β = 150° Subtract 30° to both sides

3 β + 30° - 30° = 150° - 30°

3 β = 120°

Divide both sides by 3

β = 120° / 3

β = 40°

α + β = 150°

α + 40° = 150° Subtract 40° to both sides

α + 40° - 40° = 150° - 40°

α = 110°

α = 110° , β = 40°

I don't know what is chapter lines.

Step 1: Let's assume the smaller angle is x.

Step 2: According to the problem, the larger angle is 30 more than twice the smaller angle. So, the larger angle is 2x + 30.

Step 3: We are given that the two angles are adjacent and form an angle of 150 degrees. This means the sum of the two angles is 150 degrees.
So, x + (2x + 30) = 150.

Step 4: Simplify the equation by combining like terms:
3x + 30 = 150.

Step 5: Subtract 30 from both sides of the equation:
3x = 150 - 30,
3x = 120.

Step 6: Divide both sides of the equation by 3 to solve for x:
x = 120 / 3,
x = 40.

Step 7: Now substitute the value of x back into the expression for the larger angle:
2x + 30 = 2(40) + 30,
2x + 30 = 80 + 30,
2x + 30 = 110.

Step 8: Therefore, the smaller angle is 40 degrees and the larger angle is 110 degrees.

To find the angles, let's assume the smaller angle as 'x'.

According to the given information, the larger angle is 30 more than twice the smaller angle.

So, the larger angle = 2x + 30.

We also know that when two adjacent angles are added, they form a straight angle of 180 degrees.

Therefore, the equation will be: x + (2x + 30) = 180.

Simplifying this equation, we get: 3x + 30 = 180.

Subtracting 30 from both sides, we have: 3x = 150.

Dividing both sides by 3, we get: x = 50.

So, the smaller angle is 50 degrees.

Now, we can substitute this value of x into the expression for the larger angle: 2x + 30.

Therefore, the larger angle = 2 * 50 + 30 = 130 degrees.

Hence, the two angles are 50 degrees and 130 degrees.