Fillable Online Finding Angle Measures Fax Email Print - pdfFiller - Free Printable

I can't view or analyze images directly, so I can't see the specific figures or problems in your uploaded image. However, based on the text you've provided, I can help you solve the problems listed in the worksheet titled "Finding Angle Measures".

Let me go through each problem and solve them step by step, assuming standard geometric principles and relationships.

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Part 1: Finding Missing Angle Measures

#### Problem 1:
> Find the missing measure in each figure. Keep the angle relationships in mind.

We need to use angle relationships such as:
- Vertical angles: Equal
- Supplementary angles: Add to 180°
- Complementary angles: Add to 90°
- Linear pairs: Adjacent angles that form a straight line → sum to 180°

But since no figures are visible, I'll assume typical configurations for each.

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#### Problem 6:
> ∠A and ∠B are vertical angles. If the measure of ∠A is 125°, find the measure of ∠B.

✔ Solution:
Vertical angles are congruent (equal).

So,
$$
\angle B = \angle A = 125^\circ
$$

Answer: $ \boxed{125^\circ} $

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#### Problem 7:
> ∠A and ∠B are complementary angles. If the measure of ∠A is 45°, find the measure of ∠B.

✔ Solution:
Complementary angles add up to 90°.

$$
\angle B = 90^\circ - 45^\circ = 45^\circ
$$

Answer: $ \boxed{45^\circ} $

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#### Problem 8:
> ∠P and ∠Q are supplementary angles. If the measure of ∠P is 98°, find the measure of ∠Q.

✔ Solution:
Supplementary angles add up to 180°.

$$
\angle Q = 180^\circ - 98^\circ = 82^\circ
$$

Answer: $ \boxed{82^\circ} $

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#### Problem 9:
> ∠A and ∠B form a linear pair. If the measure of ∠A is 112°, find the measure of ∠B.

✔ Solution:
Linear pairs are adjacent angles forming a straight line → sum to 180°.

$$
\angle B = 180^\circ - 112^\circ = 68^\circ
$$

Answer: $ \boxed{68^\circ} $

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Part 2: Using Algebra to Solve for Missing Measures

#### Problem 10:
> If $ m\angle PQT = 3x + 45^\circ $ and $ m\angle RQS = 6x - 25^\circ $, find the measure of $ \angle RQS $.

Assuming these angles are vertical angles (common setup), they are equal:

$$
3x + 45 = 6x - 25
$$

Solve for $ x $:

$$
45 + 25 = 6x - 3x \\
70 = 3x \\
x = \frac{70}{3} \approx 23.33
$$

Now plug into $ m\angle RQS = 6x - 25 $:

$$
6 \left( \frac{70}{3} \right) - 25 = 140 - 25 = 115^\circ
$$

Answer: $ \boxed{115^\circ} $

> ⚠️ Note: This assumes $ \angle PQT $ and $ \angle RQS $ are vertical angles. If not, more context is needed.

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#### Problem 11:
> If $ \overline{AB} \perp \overline{CD} $, $ m\angle DXE = 3x + 2 $, and $ m\angle EXC = x + 8 $, find the measure of $ \angle DXE $.

Since $ AB \perp CD $, they intersect at 90°, so angles around the point form right angles.

Assume $ \angle DXE $ and $ \angle EXC $ are adjacent angles forming a right angle (i.e., together make 90°):

$$
(3x + 2) + (x + 8) = 90 \\
4x + 10 = 90 \\
4x = 80 \\
x = 20
$$

Now find $ m\angle DXE $:

$$
3(20) + 2 = 60 + 2 = 62^\circ
$$

Answer: $ \boxed{62^\circ} $

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#### Problem 12:
> If $ m\angle KMN = 8x - 5 $ and $ m\angle HNQ = 4x - 19 $, find the measure of $ \angle KMN $.

This depends on the diagram. Common setups involve:
- Vertical angles
- Linear pairs
- Perpendicular lines

If $ \angle KMN $ and $ \angle HNQ $ are vertical angles, then:

$$
8x - 5 = 4x - 19 \\
8x - 4x = -19 + 5 \\
4x = -14 \\
x = -3.5
$$

Negative angle? Not possible.

So likely they are supplementary (linear pair or straight line):

$$
(8x - 5) + (4x - 19) = 180 \\
12x - 24 = 180 \\
12x = 204 \\
x = 17
$$

Now find $ m\angle KMN $:

$$
8(17) - 5 = 136 - 5 = 131^\circ
$$

Answer: $ \boxed{131^\circ} $

> ✔ This makes sense — positive and reasonable.

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Summary of Answers:

| Problem | Answer |
|--------|--------|
| 6 | $ 125^\circ $ |
| 7 | $ 45^\circ $ |
| 8 | $ 82^\circ $ |
| 9 | $ 68^\circ $ |
| 10 | $ 115^\circ $ |
| 11 | $ 62^\circ $ |
| 12 | $ 131^\circ $ |

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If you can describe the diagrams or clarify any assumptions (e.g., which angles are vertical, adjacent, etc.), I can refine the solutions further!