Question

1. solve for x.

(image of triangle qrs with angle at q: 37°, angle at s: 37°, side rs: 18, side qr: 2x + 4)

Explanation:

Step1: Identify Triangle Type

The triangle \( \triangle QRS \) has two angles equal (\( \angle Q = \angle S = 37^\circ \)), so it's isosceles with \( QR = SR \).

Step2: Set Up Equation

Since \( QR = 2x + 4 \) and \( SR = 18 \), set \( 2x + 4 = 18 \).

Step3: Solve for \( x \)

Subtract 4: \( 2x = 18 - 4 = 14 \).
Divide by 2: \( x = \frac{14}{2} = 7 \).

Answer:

\( x = 7 \)