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It looks like you've uploaded an image with two geometry problems related to finding missing angles. Let's break them down:

### Problem 1:
The figure contains two parallel lines, **ℓ** and **m**, with a transversal **t**. The angle of **75°** is formed by **t** and **ℓ**. We are asked to find the missing angles.

- **75°** and the missing angle on the same side of the transversal and inside the parallel lines are **consecutive interior angles**, which add up to **180°**.
- The missing angle would be **180° - 75° = 105°**.

### Problem 2:
This is a quadrilateral **ABCD** with angles **80°** at **∠DAB** and **70°** at **∠ABC**. To find the missing angles, we know the sum of interior angles of any quadrilateral is **360°**. So:

- **∠DAB + ∠ABC + ∠BCD + ∠CDA = 360°**.
- **80° + 70° + ∠BCD + ∠CDA = 360°**.
- Simplifying: **150° + ∠BCD + ∠CDA = 360°**.
- So, **∠BCD + ∠CDA = 210°**.
  
Since **∠BCD** and **∠CDA** are consecutive angles on the same side of the transversal and inside the quadrilateral, they must be supplementary. Hence, each angle is **105°** (because **210° ÷ 2 = 105°**).

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Would you like a more detailed explanation of any of these steps, or is there anything else you'd like to explore?

Here are some related questions:
1. How do you calculate angles in polygons other than quadrilaterals?
2. What is the relationship between alternate interior angles?
3. What other properties can be used to solve for unknown angles in parallel lines and transversals?
4. How does the concept of supplementary angles apply in different geometrical shapes?
5. How do you find missing angles in triangles when some angles are given?

Tip: Always remember that the sum of interior angles in any polygon can be calculated with the formula **(n - 2) × 180°**, where **n** is the number of sides.

Find the measures of the missing angles in two geometry problems involving parallel lines and a quadrilateral.

Learn how to solve geometry problems involving missing angles in parallel lines and quadrilaterals. This problem involves key concepts such as consecutive interior angles and the sum of angles in quadrilaterals. Suitable for students in Grades 7-9.

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