Question

In APQR, PR is extended through point R to point S, mZQRS = (4x – 15)°, mZRPQ = (x + 1)², and mZPQR = (x - 2). Find mZRPQ.

Answer 1

The measure of angle ZRPQ can be found by setting up an equation using the sum of angles in triangle APQR and solving for x, which can then be substituted back into the given expression for angle ZRPQ.

Step-by-step explanation:

To find the measure of angle ZRPQ, we can use the properties of the triangle and the straight line going through points P, R, and S. In triangle APQR, the sum of the angles should add up to 180°. Therefore, we can set up an equation:

m∠PQR + m∠PRQ + m∠RPQ = 180°

(x - 2) + (4x - 15) + (x + 1)² = 180°

Now, we expand and solve for x:

Substitute x into the expression for m∠RPQ and solve to find the measure of angle ZRPQ.

The complete question is: In APQR, PR is extended through point R to point S, mZQRS = (4x – 15)°, mZRPQ = (x + 1)², and mZPQR = (x - 2). Find mZRPQ. is:

Answer 2

To find the value of mZRPQ, set up an equation using the given angle measures of APQR and solve for x. Substitute the value of x into the equation for mZRPQ to find the measure of the angle.

Step-by-step explanation:

To find the value of mZRPQ, we can use the fact that the sum of the angles in a triangle is 180 degrees. Since mZQRS is given as (4x - 15)°, mZRPQ as (x + 1)², and mZPQR as (x - 2), we can set up the following equation:

(4x - 15) + (x + 1)² + (x - 2) = 180

Simplifying the equation gives:

4x - 15 + x² + 2x + 1 + x - 2 = 180

Combining like terms and rearranging the equation gives:

x² + 7x - 196 = 0

Using the quadratic formula or factoring method, we can solve for x. Once we find the value of x, we can substitute it into the equation for mZRPQ to find the measure of the angle.