Question

qs is tangent to ⊙p. what is m∠p?
s
q
30°
p
m∠p = \boxed{\space}°
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work it out
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Explanation:

Step1: Use the property of tangent - radius

A tangent to a circle is perpendicular to the radius at the point of tangency. So, \( \angle PQS=90^{\circ}\).

Step2: Use the angle - sum property of a triangle

In \(\triangle PQS\), we know that the sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle P = x\). Then, using the formula \(m\angle P+m\angle Q + m\angle S=180^{\circ}\).
We substitute \(m\angle Q = 90^{\circ}\) and \(m\angle S=30^{\circ}\) into the formula: \(x + 90^{\circ}+30^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Simplify the equation \(x+120^{\circ}=180^{\circ}\). Subtract \(120^{\circ}\) from both sides: \(x=180^{\circ}- 120^{\circ}\).

Answer:

\(60\)