The image contains several geometric diagrams with labeled angles and lengths. Let's go through each numbered question in the image step-by-step.

10. Triangle with angles and lengths

• We are given:

  • $\angle D = 15^\circ$, $\angle A = 38^\circ$
  • The side opposite $\angle D$ is $K = 20$, and the side opposite $\angle A$ is $E = 21$.

  Find: Unknown side or angle using triangle relationships (e.g., sum of angles or law of sines/cosines).

11. Intersecting triangles with marked angles

• We are given angles:
  • $\angle K = 87^\circ$, $\angle G = 68^\circ$, $\angle J = 95^\circ$, and $\angle H = 72^\circ$.
  • Note: Relationships between angles (e.g., supplementary or vertically opposite) might be used here to find unknowns.

14. Triangle bisector problem

• Given:

  • $\angle QPT = 42^\circ$, $\angle PQS = 58^\circ$.
  • $PR$ bisects $\angle QPT$.

  Find: Relationships due to the angle bisector theorem or complementary angle properties.

15. Triangles with congruency and markings

• The triangles are labeled $BMR$ and $PLZ$.
• Congruency markings (tick marks) indicate relationships between sides and angles. Solve for missing lengths or angles using congruence rules (e.g., SSS, SAS).

Would you like detailed solutions for a specific question, or should I solve them all step-by-step?

Expanding Questions:

1. Can we use the law of sines to find the unknown in question 10?
2. How do supplementary angles help in solving question 11?
3. How does the angle bisector theorem relate to the configuration in question 14?
4. What congruence rules (e.g., SSS, SAS) apply to the triangles in question 15?
5. Can all these questions be solved with basic geometric properties alone?

Tip: Always check for known relationships like the sum of angles in a triangle ($180^\circ$) or congruence properties when solving geometry problems.