Answer:
6. ∠PVU = 58°
7. y = 74°
Step-by-step explanation:
Question 6
Angles on a straight line sum to 180°.
⇒ ∠USP + ∠PSV = 180°
⇒ 148° + ∠PSV = 180°
⇒ 148° + ∠PSV - 148° = 180° - 148°
⇒ ∠PSV = 32°
The interior angle of a rectangle at each vertex is 90°.
⇒ ∠VPS = 90°
Interior angles of a triangle sum to 180°.
⇒ ∠PVS + ∠PSV+ ∠VPS = 180°
⇒ ∠PVS + 32° + 90° = 180°
⇒ ∠PVS + 122° = 180°
⇒ ∠PVS + 122° - 122° = 180° - 122°
⇒ ∠PVS = 58°
From inspection of the given diagram:
⇒ ∠PVU = ∠PVS
⇒ ∠PVU = 58°
Question 7
Opposites sides of a rectangle are parallel.
Therefore, GF is parallel to AB:
⇒ ∠CFG = ∠CBA = 32°
Interior angles of a triangle sum to 180°.
⇒ ∠FGC + ∠GCF + ∠CFG = 180°
⇒ y + 74° + 32° = 180°
⇒ y + 106° = 180°
⇒ y + 106° - 106° = 180° - 106°
⇒ y = 74°
