To solve the missing angles on these triangles, let's analyze each one step-by-step.

Top Left Triangle (m∠q)

• It’s a right triangle where one angle is 45°.
• In a triangle, the sum of angles equals 180°.
• Since one angle is 90° and another is 45°, we calculate: $\text{m∠q} = 180° - 90° - 45° = 45°$ ✅ m∠q = 45° (already shown correctly).

Top Right Triangle (m∠r)

• The triangle has one angle as 65°.
• It is an isosceles triangle, meaning two angles are equal.
• Using the angle sum property: $180° - 65° = 115°$
• Split 115° equally for the two equal angles: $\text{m∠r} = \frac{115°}{2} = 57.5°.$ ✅ Approximated m∠r = 57° (rounded and shown correctly).

Bottom Left Triangle (m∠h)

• The exterior angle given is 52°, and it forms a linear pair with angle h.
• Linear pairs add up to 180°: $\text{m∠h} = 180° - 52° = 128°.$ ✅ m∠h = 128°.

Bottom Right Triangle (m∠g)

• One angle is 60°, and it’s an isosceles triangle, so two angles are equal.
• Let the equal angles be $g$. Use the angle sum property: $60° + 2g = 180°.$
• Solve for $g$: $2g = 180° - 60° = 120° \quad \Rightarrow \quad g = \frac{120°}{2} = 60°.$ ✅ m∠g = 60°.

Summary of Solutions:

1. m∠q = 45°
2. m∠r = 57°
3. m∠h = 128°
4. m∠g = 60°

Let me know if you need further explanations!

Related Questions:

1. What is the angle sum property of a triangle?
2. How do you calculate angles in an isosceles triangle?
3. What is the concept of exterior angles in triangles?
4. Can you explain the concept of linear pairs in geometry?
5. How can you find unknown angles in right triangles?

Tip: Always check if the triangle has specific properties (isosceles, equilateral, or right triangle) to simplify angle calculations.