Question

Given triangle QRS ~ triangle XYZ and line XY is 15, line YZ is 9, and line SX is 12, what is the value of angle Q?

Option 1: 36 degrees
Option 2: 45 degrees
Option 3: 60 degrees
Option 4: 72 degrees

Answer 1

To find the value of angle Q in triangle QRS, we can use similar triangles and set up a proportion. Solving the proportion gives us the value of angle Q as 45 degrees.

Step-by-step explanation:

To find the value of angle Q, we can use the fact that corresponding angles in similar triangles are congruent.

We know that triangle QRS is similar to triangle XYZ. Given that line XY is 15, line YZ is 9, and line SX is 12, we can set up the following proportion:

(QR / XY) = (RS / YZ)

Let's substitute the known values into the equation:

(QR / 15) = (RS / 9)

Let's cross multiply:

9QR = 15RS

Now, let's solve for RS in terms of QR:

RS = (9/15) * QR = (3/5) * QR

Since the ratios of the corresponding sides of similar triangles are equal, we can say:

RS/QR = YZ/XY = 9/15

Let's solve this equation for QR:

(3/5) * QR / QR = 9/15

3/5 = 9/15

3 * 15 = 5 * 9

45 = 45

Since both sides are equal, we know that the value of angle Q is the same as angle X, which is 45 degrees.