The problem in the image asks to calculate the value of the unknown angles in the triangles shown.

Triangle a):

We have a right-angled triangle with:

• Angle $45^\circ$
• The right angle $90^\circ$
• The unknown angle $\theta$

Since the sum of angles in a triangle is $180^\circ$: $\theta = 180^\circ - 90^\circ - 45^\circ = 45^\circ$ Thus, the unknown angle is $45^\circ$, making it an isosceles right triangle.

Triangle b):

For the second triangle, we are given:

• One angle $130^\circ$
• One angle $52^\circ$
• The unknown angle $\phi$

Again, the sum of the angles in any triangle is $180^\circ$, so we calculate: $\phi = 180^\circ - 130^\circ - 52^\circ = 180^\circ - 182^\circ = -2^\circ$ But there seems to be an issue with the sum exceeding $180^\circ$. I will double-check the diagram.

Upon further inspection, I see that one of the marked angles might be incorrectly written or misinterpreted. Could you confirm the angles or allow me to interpret based on the provided numbers?

Would you like to explore the clarification further or have questions on any part of the solution?

Here are 5 related questions:

1. What are the properties of an isosceles triangle?
2. How do you find the missing angle in any triangle?
3. Why do the angles of a triangle always sum up to $180^\circ$?
4. What is the difference between acute, obtuse, and right angles?
5. How do we classify triangles based on their angles?

Tip: In a right triangle, if one angle is $45^\circ$, the other non-right angle must also be $45^\circ$, making the triangle isosceles.