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The two parallel lines $L$ and $M$ are intersected by $T$, see Figure $14 .$ Find all the indicated angles.

$$\alpha=\theta=115^{\circ}, \beta=\delta=\eta=65^{\circ}$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 9

Elements of Geometry

Derivatives

Oregon State University

Harvey Mudd College

University of Nottingham

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

02:04

Find the measure of angles…

01:44

01:39

Given the following inform…

03:11

In the following figure, l…

04:19

In each figure, find the m…

07:51

for this problem. We have two parallel lines l and M. And they are crossed by a trans versa, which I'm tracing in red here. So a trans Verceles crosses over a set of parallel lines. Our goal for this problem is to figure out the degrees of as many angles as we can. Now, fortunately, were given 1 65 degrees right there. Unfortunately, that's the only one we know. The other angles we need to find are marked with Greek letters. I have Alpha. I've gotta Fada, I have a to over here and I have Delta right there. So how do we find these? Well, there's a couple of things we know about a Trans Verceles crossing these parallel lines. First, we have corresponding angles. Okay? Corresponding angles are equal to each other and corresponding angles. Angles that appear in the same spot on each intersection. For example, my 65 degrees and my delta are both in that same corner. If I look at the transfer cell and l and the transfer cell and M 65 degrees in Delta occupy the same space, so Delta is going to be 65 degrees. Okay, now we also know vertical angles are equal. Vertical angles are angles that are across from each other at an intersection of two straight lines. So 65 beta are vertical. Angles are across from each other, so beta is going to be 65 degrees as well. Take a look at ADA. Ada and Delta are vertical angles, so that's also 65. We can also say that Beta and ADA are corresponding angles. They occur in the same place in that intersection. So we've been able to label three of our five unknown angles the last two. We're going to need one more definition and for that we're going to talk about supplementary angles. Supplementary angles are angles that add up to 180 degrees, and together they make a straight angle and that's going to look something like this. If I have two angles that go together to make a straight line, I have a green angle here. I have a blue angle. Here they add up to 180 This right here that this straight line that's 100 and 80 degrees. Well, we can use that definition to find our missing too because Alpha and that 65 degrees together make up a straight angle. They are supplementary, so they have to add up to 180 degrees. Which means alpha has to be 115. 1 15 plus 65 is 1 80. And now Alpha and theta are across from each other. They are vertical angles, so they are equal.

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