Question

if m∠pqr = (3x + 5)°, m∠rqs = (2x - 10)°, and m∠pqs = 100°, find x.

Explanation:

Step1: Relate angles (angle addition)

Since \( \angle PQR \) and \( \angle RQS \) form \( \angle PQS \), we have \( m\angle PQR + m\angle RQS = m\angle PQS \). Substituting the given expressions:
\( (3x + 5) + (2x - 10) = 100 \)

Step2: Simplify and solve for \( x \)

Combine like terms: \( 3x + 2x + 5 - 10 = 100 \)
\( 5x - 5 = 100 \)
Add 5 to both sides: \( 5x = 105 \)
Divide by 5: \( x = \frac{105}{5} = 21 \)

Answer:

\( x = 21 \)