Question

Please help numbers 28, 30, 32, 34

Answer 1

28.

The path of any fair ball will divide the 90° angle between foul lines into complementary angles. The angle with the first-base foul line is ...

... 90° -27° = 63°

30.

The attached picture shows the two angles "constructed" using a protractor. It is not possible to construct a 97° angle with compass and straight-edge

32.

Let x represent the measure of the complement. Then the angle that is 6° less than the meaure of the complement is x-6°. The angle and its complement total 90°, so we have ...

... (x-6°) + (x) = 90°

... 2x - 6° = 90° . . . . . simplify

... 2x = 96° . . . . . . . . .add 6°

... x = 48° . . . . . . . . . . divide by 2

... (x-6°) = 48°-6° = 42°

The angles are 42° and 48°.

34.

Let x represent the measure of the angle. Then its supplement is 180°-x, and half that is (180°-x)/2. The angle is 3° more than this, so we have

... x = (180° -x)/2 +3°

... x -3° = (180° -x)/2 . . . . subtract 3°

... 2x -6° = 180° -x . . . . . .multiply by 2

... 3x -6° = 180° . . . . . . . .add x

... x - 2° = 60° . . . . . . . . . divide by 3 to get x by itself

... x = 62° . . . . . . . . . . . . add 2°

... The supplementary angle is 180° -62° = 118°, half of which is 59°.

One angle is 62°; half the measure of its supplement is 59°; it supplement is 118°.