Answer:
∠e = 105° because ∠e and the 105° angle are vertically opposite angles
∠h = 75° because ∠h and the 105° angle are supplementary angles
∠f = ∠h = 75° because ∠f and ∠h are vertically opposite angles
∠c = 105° because ∠c and the 105° are corresponding angles
∠b = 75° because ∠b and ∠f are corresponding angles
∠a = 105° because ∠a and ∠e are corresponding angles
∠d = 75° because ∠d and ∠h are corresponding angles
Step-by-step explanation:
The given diagram includes two parallel lines having a common transversal that crosses both (parallel) lines
By sing angle properties, we have;
∠e = 105° because ∠e and the 105° angle are vertically opposite angles formed by the same two straight lines and are therefore always equal
∠h = 180° - 105° = 75° because ∠h and the 105° angle are angles that form a straight line and are therefore supplementary angles which are angles that sum up to 180°. Therefore, ∠h + 105° = 180°, therefore ∠h = 75°
∠f = ∠h = 75° because ∠f and ∠h are vertically opposite angles
∠c = 105° because ∠c and the 105° are corresponding angles and corresponding angles are equal
Similarly, we have;
∠b = ∠f = 75° because ∠b and ∠f are corresponding angles
∠a = ∠e = 105° because ∠a and ∠e are corresponding angles
∠d = ∠h = 75° because ∠d and ∠h are corresponding angles
