14 two consecutive angles of a parallelogram have measures x...

14. Two consecutive angles of a parallelogram have measures (x + 30) and (2x - 30). What is the measure of the larger angle? a. 30° b. 80° c. 100° d. 140° 15. Which of the following statements is true? a. A trapezoid can have four equal sides. b. A trapezoid can have three right angles. c. The base angles of an isosceles trapezoid are congruent. d. The diagonals of an isosceles trapezoid bisect each other. 16. The diagonals of an isosceles trapezoid are represented by (4x - 47) and (2x + 31). What is the value of x? a. 37 b. 39 c. 107 d. 109 17. In a parallelogram KAYE, diagonals KY and AE intersect at O. If YO = 18 cm, what is the length of diagonal AE? a. 6 cm b. 9 cm c. 18 cm d. 36 cm 18. What condition will make a parallelogram WXYZ a rectangle? a. WXYZ b. WXYZ c. Angle X is a right angle. WX and YZ bisect each other.

Transcript

00:01 Okay, so if you have a parallel of them, and the consecutive angles are x plus 30, and i'm going to say 2x minus 30, because what i saw did not look right.

00:29 These two equal 180, so x plus 30 plus 2x minus 30 equals 180.

00:37 So that gives me those cancel so 3x equals 180 divided by 3 so x equals 60 so the larger angle would be 120 which is not one of your answer choices let me copy and paste this so you can see what i see so i don't know what this is supposed to say here i don't know what this is supposed to say but i know that that's x plus 30.

01:35 I don't know what this is 2x minus whatever.

01:38 I don't know what this is supposed to be, but i doubt it's supposed to be 303.

01:43 Well, maybe let me try 2x plus 30 plus 2x minus 30 equals 180.

02:04 So 3x minus 273 equals 180.

02:08 Add 273 to both sides.

02:22 453 so x equals 151 which is still not going to be an answer to us because they can't be more than 51 and that's a oh i don't know i did wrong i know i did wrong i forgot to go back and plug it in so the smaller angle is 60 plus 30 which is 90 and then 2x minus 30 so so 2 times 60 minus 30 is also 90, which is still not one of your answer choices.

03:13 However, you see how to solve it, so you can go back and rework it with whatever it's actually supposed to say.

03:22 Next, which is a true statement.

03:29 When you're talking about a trapezoid, all four sides are not equal.

03:39 That's not true.

03:40 A trapezoid has three right angles.

03:42 No, it would not have more than two congruent angles.

03:45 Well, man, i guess it could have three right angles, but not always.

04:07 So this could be true, but not always.

04:15 That's sometimes.

04:19 Not always.

04:21 The base angles are congruent.

04:22 If it's osceles, so if these two are congruent, then these two are congruent.