Obtuse angles A and B are in standard position. Point P(-3,4) is on the terminal arm of angle A. Point Q(-9,12)is on the terminal arm of angle B. How are the measures of angles A and b related?

Please explain...

If you put P and Q on the same grid, did you notice that OQ is an extension of OP ?

so the angle formed by OP and OQ are the same
notice the hypotenuse of the smaller triangle is 5 by Pythagoras, and of the larger triangle it is 15

try this on your calculator:
2nd
cos
(
-3÷5
)
= to get 126.8698...°

now try:
2nd
cos
(
-9÷15
)
=
to get exactly the same angle of 126.8698...°

To understand how the measures of angles A and B are related, we first need to understand what it means for angles to be in standard position and what the terminal arm of an angle refers to.

In standard position, an angle is formed by a ray (called the initial arm) that starts at the origin (0,0) and extends towards the positive x-axis, and another ray (called the terminal arm) that rotates counter-clockwise from the initial arm.

Now let's consider the given information: point P(-3,4) is on the terminal arm of angle A, and point Q(-9,12) is on the terminal arm of angle B.

We can determine the lengths of the terminal arms of angles A and B using the distance formula, which is the Pythagorean theorem applied to find the hypotenuse of a right triangle.

For angle A:
Length of terminal arm of angle A = √((-3)^2 + 4^2) = √(9 + 16) = √25 = 5

For angle B:
Length of terminal arm of angle B = √((-9)^2 + 12^2) = √(81 + 144) = √225 = 15

Now, let's consider the relation between the measures of angles A and B. The measure of an angle is typically given in degrees or radians.

Since angle A and angle B are both obtuse angles, we can conclude that they are greater than 90 degrees. However, we can't determine a specific angle measure just by knowing the lengths of their terminal arms and that they are obtuse.

In summary, the length of the terminal arm of angle A is 5 units, and the length of the terminal arm of angle B is 15 units. However, without further information, we cannot determine how the measures of angles A and B are related.