Question

m∠a = 50°, m∠j = 45°, and m∠s = 16x + 5.
what is the value of x?

Explanation:

Step1: Identify congruent triangles

The two triangles have corresponding sides marked equal (congruent markings), so the triangles are congruent. Thus, corresponding angles are equal. So, \( m\angle W = m\angle S \).

Step2: Find \( m\angle W \) using triangle angle sum

In \( \triangle CJW \), sum of angles in a triangle is \( 180^\circ \). So, \( m\angle C + m\angle J + m\angle W = 180^\circ \). But since the triangles are congruent, \( m\angle C = m\angle A = 50^\circ \), \( m\angle J = 45^\circ \). So, \( 50^\circ + 45^\circ + m\angle W = 180^\circ \).
\( m\angle W = 180^\circ - 50^\circ - 45^\circ = 85^\circ \).

Step3: Set \( m\angle S = m\angle W \) and solve for \( x \)

Since \( m\angle S = m\angle W = 85^\circ \), and \( m\angle S = 16x + 5 \). So, \( 16x + 5 = 85 \).
Subtract 5 from both sides: \( 16x = 85 - 5 = 80 \).
Divide both sides by 16: \( x = \frac{80}{16} = 5 \).

Answer:

\( x = 5 \)