Question

click and drag to draw a ray from the yellow dot. to redraw, click and drag from the yellow dot again. m∠pqr = 102°, m∠pqs = 51°, m∠rqs = 51°. which of the following statements is true? answer: m∠pqs = 1/2 (m∠rqs), m∠pqs = m∠rqs, m∠pqr = m∠rqs, m∠pqr = m∠pqs

Explanation:

Step1: Identify given angle - measures

Given \(m\angle PQR = 102^{\circ}\), \(m\angle PQS=51^{\circ}\), \(m\angle RQS = 51^{\circ}\)

Step2: Check each option

• Option 1: \(\frac{1}{2}(m\angle RQS)=\frac{1}{2}\times51^{\circ}=25.5^{\circ}

eq m\angle PQS\)

• Option 2: \(m\angle PQS = 51^{\circ}\) and \(m\angle RQS=51^{\circ}\), so \(m\angle PQS = m\angle RQS\)
• Option 3: \(m\angle PQR = 102^{\circ}

eq m\angle RQS = 51^{\circ}\)

• Option 4: \(m\angle PQR = 102^{\circ}

eq m\angle PQS = 51^{\circ}\)

Answer:

\(m\angle PQS = m\angle RQS\)