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°).

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.