Question

1. right angles xpf and bwy are shown. ray ph is inside ∠xpf, such that m∠hpf = 39° and m∠hpf = m∠kwy. what is m∠bwk?

Explanation:

Step1: Identify right angle measure

A right angle is \(90^\circ\), so \(m\angle BWY = 90^\circ\) (since \(\angle BWY\) is a right angle) and \(m\angle HPF = 39^\circ\), and \(m\angle HPF = m\angle KWY\), so \(m\angle KWY = 39^\circ\).

Step2: Calculate \(m\angle BWK\)

We know that \(m\angle BWY = m\angle BWK + m\angle KWY\). Rearranging for \(m\angle BWK\), we get \(m\angle BWK = m\angle BWY - m\angle KWY\). Substituting the values, \(m\angle BWK = 90^\circ - 39^\circ\).

Step3: Compute the result

\(90 - 39 = 51\), so \(m\angle BWK = 51^\circ\).

Answer:

\(51^\circ\)