12. Igram for questions 12-14. Identify the special name for...

12. Igram for questions 12-14. Identify the special name for (angle 3) and (angle 10). (A) consecutive interior (B) alternate exterior (C) alternate interior (D) corresponding 13. Given (angle 1 cong angle 5), which postulate or theorem justifies that (p parallel q)? (A) Converse of Corresponding Angles Postulate (B) Consecutive Interior Angles Converse (C) Alternate Exterior Angles Converse (D) Alternate Interior Angles Converse 14. If (mangle 4 = 7x - 20) and (mangle 8 = 5x + 18), find the value of (x) so that (p parallel q). (A) 219 (B) -1 (C) 1 (D) 19 15. If A, B, and N are collinear and (AB + BN = AN), which point is between the other two points? (A) A (B) B (C) N (D) cannot tell 16. If (a + b le 8) and (a = 2), then (b le 5). Which of the following would be a counterexample? (A) (b = 3) (B) (b = 5) (C) (b = 6) (D) (b = a) 17. Which law can be used to determine that the conclusion is valid based on the given statements? Given: If an angle is acute, then it cannot be obtuse. (angle A) is acute. Conclusion: (angle A) cannot be obtuse. (A) Law of Detachment (B) Law of Syllogism (C) Law of Converse (D) The conclusion is not valid.

Transcript

00:01 Okay, so we are given a number of problems to solve and so i will go through each of these step by step the first one says identify a special name for angle three and angle 10 well angle three is here angle 10 is here we notice that these two are on the same side of the transversal so what that means is they are consecutive interior they are inside the two lines that the transversal intersects, so that makes them interior.

00:36 Consecutive means next to each other.

00:41 Okay? the next problem says, given angle one and angle five, given angle one is congruent angle five, which theorem justifies that p is parallel to q.

00:53 So here's angle one, here's angle five, and they are both created by transversal r, which intersects p and q.

01:04 Based on what we know about transversals and the lines that they intersect, these two angles would be considered corresponding angles.

01:15 And the original statement or conditional regarding parallel lines and transversals and corresponding angles would be that if two lines are parallel, then corresponding angles are congruent.

01:31 And in this case, we're saying if the two angles that are corresponding are congruent, then the lines are parallel.

01:39 That's going to be the converse because we switched our hypothesis and conclusion on that statement.

01:46 So that would be the converse of corresponding angles.

01:53 Okay.

01:54 And moving on to the next problem.

01:58 It says if the measure of angle 4 equals 7x minus 20.

02:01 So here's angle 4 and the measure of angle 8 equals 5x plus 18.

02:11 That's right here.

02:13 Find the value of x such that p is parallel to q.

02:17 So the first thing we would do is we would go ahead and identify that angle 4 and angle 8 are corresponding angles.

02:29 And if lines are congruent, lines are parallel, corresponding angles are congruent.

02:36 So that would mean the measure of angle 4 is equal to the measure of angle 8.

02:42 So we're going to write that equation.

02:44 Let's substitute our expression, 7x minus 20 is equal to 5x plus 18.

02:53 And we'll solve that equation using our algebra skills.

02:57 Subtract 5x from both sides.

03:01 We get 2x minus 20 equals 18.

03:06 Now we'll go ahead and add 20 to each side.

03:11 We get 2x equals 38, divide by 2, and we get x equals 19.

03:19 So now we know that the value of x is 19, and we can double check that by substituting in 19 for x on both expressions.

03:32 Okay, so we could say 7 times 19 minus 20.

03:39 That equals 113.

03:42 So that's the measure of angle 4.

03:44 The measure of angle 8 was 5 times 19 plus 18...

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