Question

which are the correct measures of the indicated angles? select one: a. <w = 103°, <x =103°, <y = 77° b. <w = 77°, <x =77°, <y = 103° c. <w = 103°, <x =77°, <y = 77° d. <w = 77°, <x =103°, <y = 103°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle \(y\) and the \(103^{\circ}\) angle are vertical angles, so \(y = 103^{\circ}\).

Step2: Use supplementary - angle property

Angle \(y\) and angle \(w\) are supplementary (a linear - pair), so \(y+w = 180^{\circ}\). Substituting \(y = 103^{\circ}\), we get \(w=180 - 103=77^{\circ}\).

Step3: Use corresponding - angle property

Angle \(x\) and angle \(y\) are corresponding angles for the parallel lines, so \(x = y=103^{\circ}\).

Answer:

d. \(\angle w = 77^{\circ},\angle x = 103^{\circ},\angle y = 103^{\circ}\)