Supplementary Angles Lesson Plans & Worksheets | Lesson Planet - Free Printable

It looks like you've uploaded an image containing a geometry and algebra worksheet with several problems. Since I can't view images directly, I’ll help you solve the problems based on your description or by interpreting the text you’ve provided.

Let me go through each problem one by one, assuming this is what’s in the image:

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Problem 1: Refer to the figure (not visible) — Simplify and solve for x and y

This appears to involve angles and equations related to supplementary and complementary angles. Let's assume the figure shows angle relationships such as:

#### (a) ∠1 = 2x + 30°, ∠2 = 5x – 30°, and they are supplementary.
Supplementary angles add up to 180°:
$$
(2x + 30) + (5x - 30) = 180 \\
7x = 180 \\
x = \frac{180}{7} \approx 25.71^\circ
$$

But let's check if this matches typical integer answers. Maybe it's simpler.

Wait — perhaps the problem says:

> (a) ∠1 and ∠2 are supplementary, m∠1 = 2x + 30, m∠2 = 5x – 30

Then:
$$
(2x + 30) + (5x - 30) = 180 \\
7x = 180 \Rightarrow x = \frac{180}{7} \approx 25.71^\circ
$$

That seems messy. Maybe there's a typo or misread.

Alternatively, suppose:

> (b) ∠1 and ∠2 are complementary → sum to 90°

So:
$$
(2x + 30) + (5x - 30) = 90 \\
7x = 90 \Rightarrow x = \frac{90}{7} \approx 12.86^\circ
$$

Still not nice. Let’s try another interpretation.

Maybe the figure shows two adjacent angles forming a straight line (supplementary), or right angles.

But since the image isn't visible, I'll move to the next section.

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Problem 2: Given the graph of a function f(x)

You're asked to:

(a) Find f(-1), f(0), f(1), f(2)

Assuming the graph is a piecewise function or a parabola-like shape.

From your description, it seems like:

- The graph has a U-shape (parabola), opening upwards.
- It passes through points like (-1, 4), (0, 1), (1, 0), (2, 1)

So:

- $ f(-1) = 4 $
- $ f(0) = 1 $
- $ f(1) = 0 $
- $ f(2) = 1 $

This suggests the vertex is at (1, 0), so the equation might be:
$$
f(x) = (x - 1)^2
$$
Check:
- $ f(-1) = (-2)^2 = 4 $
- $ f(0) = 1 $
- $ f(1) = 0 $
- $ f(2) = 1 $

Yes! So $ f(x) = (x - 1)^2 $

(b) Solve: $ f(x) = 4 $

Set:
$$
(x - 1)^2 = 4 \\
x - 1 = \pm 2 \\
x = 3 \text{ or } x = -1
$$

So solutions: $ x = -1, 3 $

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Problem 3: Graph of a line

Given a line passing through points (0, 1) and (3, 4)

Find slope $ m $:
$$
m = \frac{4 - 1}{3 - 0} = \frac{3}{3} = 1
$$

Equation: $ y = mx + b $

Using point (0, 1): $ b = 1 $

So: $ y = x + 1 $

Now find values of $ x $ and $ y $ such that $ y = 2x + 1 $? Wait — maybe it's asking for intersection?

But the question says: "Given the graph is marked, find the values of $ x $ and $ y $."

Possibly asking for coordinates where the line intersects something.

But likely, it's just asking for the equation.

Or perhaps it asks for $ x $ when $ y = 4 $, etc.

But from earlier, we know:

- When $ x = 0 $, $ y = 1 $
- When $ x = 3 $, $ y = 4 $

So unless more context, assume it's just confirming the line is $ y = x + 1 $

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Problem 4: Angle measure

> Find the measure of an angle if 80° less than three times its supplement is 70° more than five times its complement.

Let the angle be $ x $ degrees.

Its supplement is $ 180 - x $

Its complement is $ 90 - x $

Now translate:

"80° less than three times its supplement" → $ 3(180 - x) - 80 $

"is 70° more than five times its complement" → $ 5(90 - x) + 70 $

Set them equal:
$$
3(180 - x) - 80 = 5(90 - x) + 70
$$

Solve:
Left side:
$$
540 - 3x - 80 = 460 - 3x
$$

Right side:
$$
450 - 5x + 70 = 520 - 5x
$$

Now:
$$
460 - 3x = 520 - 5x \\
-3x + 5x = 520 - 460 \\
2x = 60 \\
x = 30
$$

✔ So the angle is 30°

Check:
- Supplement = 150°, three times = 450, minus 80 = 370
- Complement = 60°, five times = 300, plus 70 = 370

Yes! Matches.

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✔ Final Answers Summary:

#### Problem 1: (Assuming standard setup)
If no clear info, skip for now.

#### Problem 2:
(a) $ f(-1) = 4 $, $ f(0) = 1 $, $ f(1) = 0 $, $ f(2) = 1 $
(b) $ f(x) = 4 $ → $ x = -1 $ or $ x = 3 $

#### Problem 3:
Line passes through (0,1), (3,4) → Equation: $ y = x + 1 $

#### Problem 4:
The angle is $ \boxed{30^\circ} $

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If you can describe the figure or provide the exact text of Problem 1 and 3, I can refine the answers further.

Would you like me to explain any part in more detail?