Math  /  Geometry

QuestionA. 1 B. 2 many angle measurements do you need to figure out the measurements of all the labeled angles the figure below? 1 2 4 3 C. 3 D. 4

Studdy Solution

STEP 1

What is this asking? If we know *some* of the angles made by two intersecting lines, how many do we *actually* need to know to figure out *all* of them? Watch out! Don't overthink it!
We're dealing with intersecting lines, so there are special relationships between the angles.

STEP 2

1. Adjacent Angles
2. Vertical Angles
3. How Many Do We *Really* Need?

STEP 3

When two lines intersect, they form adjacent angles that add up to 180180^\circ.
Think of it like a straight line being cut in two.
The two pieces together still make up the whole straight line, or 180180^\circ.

STEP 4

In our problem, angles 1\angle 1 and 2\angle 2 are adjacent.
This means: 1+2=180 \angle 1 + \angle 2 = 180^\circ So, if we know 1\angle 1, we can easily find 2\angle 2 by subtracting 1\angle 1 from 180180^\circ.

STEP 5

Vertical angles are the angles that are *opposite* each other when two lines intersect.
These angles are **always equal**!

STEP 6

In our problem, 1\angle 1 and 3\angle 3 are vertical angles.
So: 1=3 \angle 1 = \angle 3 Also, 2\angle 2 and 4\angle 4 are vertical angles, meaning: 2=4 \angle 2 = \angle 4

STEP 7

Let's say we **only** know 1\angle 1.
Because 1\angle 1 and 2\angle 2 are adjacent, and we know they add up to 180180^\circ, we can find 2\angle 2 like this: 2=1801 \angle 2 = 180^\circ - \angle 1 We also know that 1=3\angle 1 = \angle 3 (vertical angles), so we know 3\angle 3 too!
And since 2=4\angle 2 = \angle 4 (also vertical angles), we've got 4\angle 4 figured out as well!

STEP 8

So, by knowing just **one** angle, we were able to find *all* the others!
That's the power of understanding angle relationships!

STEP 9

We only need to know **one** angle measurement, so the answer is A.

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