The figure below shows a straight line ab intersected by another straight line t: write a paragraph to prove that the measure of angle 1 is equal to the measure of angle 3.

As ∠1 and ∠4 makes straight line t so their sum should be equal to 180°

∠1 + ∠4 = 180° (makes pair of supplementary angles)(1)

Similarly ∠3 and ∠4 makes straight line AB so their sum should also be equal to 180°

∠3 + ∠4 = 180° (makes pair of supplementary angles)(2)

From equations (1) and (2) we get

∠1 + ∠4 = ∠3 + ∠4 (as both were equal to 180°)

subtracting ∠4 from both sides we get

∠1 + ∠4 - ∠4 = ∠3 + ∠4 -∠4

∠1 = ∠3

Hence, proved that verticaly opposite angles ∠1 and ∠3 are equal

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40