Mary is explaining the angle relationship of the interior angles of triangles to a coworker. she states that the angles should always add up to 180°. how can mary prove that this is true? (hint: imagine taking the angles and putting them side by side.)

Answer with explanation:

To Prove: Sum of Interior angles of triangle is 180°.

Proof:

  In ΔABC

Draw line l, parallel to BC.

∠1=∠2------(1)

∠3=∠4------(2)

As lines are parallel , So Alternate Interior angles are equal.

→→Angles, ∠1,∠3, and ∠5 lie on a line.That, is they form a linear pair.Sum of Angles in linear pair is 180°.

 ∠1+∠3+∠5=180°

→∠2+∠4+∠5=180°-------[Using 1 and 2]

⇒∠A + ∠B+ ∠C=180°

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.