Answer:
m∠BWP = 46°
Step-by-step explanation:
YZXW is a quadrangle.
We know: Angles i quadrangle add up to 360°.
Therefore we have the equation:
m∠DYP + m∠CZR + m∠AXS + m∠BWQ = 360°
Substitute given measures of angles:
46° + 76° + 104° + m∠BWQ = 360°
226° + m∠BWQ = 360° subtract 226° from both sides
m∠BWQ = 134°
∠BWQ and ∠BWP are supplementary angles (add up to 180°).
Therefore
m∠BWP = 180° - 134°
m∠BWP = 46°
Other method.
m∠CZR + m∠AXS = 76° + 104° = 180°
Conclusion: YZXW is a trapezoid. Therefore CD is parallel to AB.
Therefore ∠DYP and ∠BWP are corresponding angles.
Corresponding angles have equal measures.
Therefore m∠BWP = m∠DYP = 46°
