Please answer the following questions.

Step-by-step explanation:

1. Alternate angles- Two angles are said to be alternate if they are not on the same side of the line, that intersects two other parallel lines. In the figure given above

∠1=∠8 & ∠5=∠4 (Exterior alternate angle)

∠6=∠3 & ∠2=∠7 (Interior alternate angle)

2. According to Pythagoras theorem, an essential condition for any triangle to be a right-angled triangle is (base)²+(perpendicular)²=(hypotenuse) ²

We selectively apply the given options to check which options fit in the given hypothesis.

Only (17)² = (15)² + (8) ²

3. The sum of all the interior angles of Hexagon is 6(number of sides) * 120° (measure of one interior angle)= 720°

4. In the question Height of the silo is 30 foot while the length of the shadow is 20 foot.  

Distance between the tip of the shadow to the top of the silo would be (silo height)² +(shadow)²=(distance) ²

Distance=√1300

∴Distance= 36 feet(approx.)

5. The measure of the central angle is equal to the arc it creates. Hence arc measure would be 76 °

6. Sum of the all the angles of the nonagon is 1260° while no of sides is 9

Each interior angle measures 140 °

7. In the given Figure ∠6 and ∠7 are conjugate pairs summing up to 180° (since x and y are parallel lines)

Hence ∠6 would measure 180-121=59 °