The m angle is 30 times more than twice angle B. If angle A and angle B form a linear pair find the measurement of both angles.
A linear pair are two angles that are adjacent and supplementary. They form a straight line.
So in radians: A + B = π
Or in degrees: A + B = 180°
Given: A = 30 B
Solve the solve the simultaneous equations.
4x-19/24=7/24
To find the measurements of angles A and B, we need to first understand the relationship described in the problem.
Let's assume angle A is the larger angle, while angle B is the smaller angle. According to the problem, the m angle (angle A) is 30 times more than twice angle B.
Let's represent angle B as 'x'. Then, we can express angle A in terms of angle B as follows:
Angle A = 30 * (2 * angle B) = 60 * angle B
Since angle A and angle B form a linear pair, their measures add up to 180 degrees. Mathematically, we can write it as:
Angle A + Angle B = 180 degrees
Substituting the expression we found for Angle A, we get:
60 * angle B + angle B = 180 degrees
Combining like terms, we can simplify the equation:
61 * angle B = 180 degrees
Now, let's solve for angle B by dividing both sides of the equation by 61:
angle B = 180 degrees / 61
Using a calculator or long division, we find:
angle B ≈ 2.95 degrees
Now that we know angle B, we can find angle A by substituting the value back into our expression for angle A:
Angle A = 60 * angle B ≈ 60 * 2.95 degrees
Calculating this expression, we find:
angle A ≈ 177 degrees
Therefore, angle B is approximately 2.95 degrees, while angle A is approximately 177 degrees.