https://file.aiquickdraw.com/mathbot/file/1729565815642lk4rwvb5.jpg

Let's go through each of the triangles in the image and solve the relevant problems:

### 1. Triangle with an exterior angle and two equal sides
- The triangle shows one exterior angle of \(50^\circ\) and asks for angle \(a\) inside the triangle.
- Since the two sides marked as equal indicate that this is an isosceles triangle, the two base angles will be equal.
- The sum of the interior angles in any triangle is \(180^\circ\). The exterior angle is equal to the sum of the two opposite interior angles, so:
  \[
  50^\circ = 2a
  \]
  Solving for \(a\):
  \[
  a = 25^\circ
  \]

### 2. Right triangle with a given angle of \(48^\circ\)
- The angle at the bottom right is \(90^\circ\) (since it's a right triangle).
- To find angle \(b\), use the fact that the sum of the angles in a triangle is \(180^\circ\):
  \[
  b = 180^\circ - 90^\circ - 48^\circ = 42^\circ
  \]

### 3. Right triangle with one angle given as \(40^\circ\)
- The triangle has a right angle at \(B\) and an angle of \(40^\circ\) at \(A\).
- The third angle at \(C\) is:
  \[
  C = 180^\circ - 90^\circ - 40^\circ = 50^\circ
  \]

### 4. Triangle with angles in terms of \(g\)
- The angles in the triangle are expressed as \(g\), \(2g\), and \(3g\).
- Since the sum of angles in any triangle is \(180^\circ\), we can set up the equation:
  \[
  g + 2g + 3g = 180^\circ
  \]
  Simplifying:
  \[
  6g = 180^\circ
  \]
  Solving for \(g\):
  \[
  g = 30^\circ
  \]
  Therefore, the three angles are:
  \[
  g = 30^\circ, \quad 2g = 60^\circ, \quad 3g = 90^\circ
  \]

### Summary of Results:
1. \( a = 25^\circ \)
2. \( b = 42^\circ \)
3. \( C = 50^\circ \)
4. \( g = 30^\circ \), \( 2g = 60^\circ \), \( 3g = 90^\circ \)

Would you like further details or explanations on any of these steps?

Here are five related questions to expand your understanding:
1. How would the solution change if the triangle in problem 1 were scalene instead of isosceles?
2. In problem 2, can you calculate the lengths of sides using trigonometry given one side length?
3. How does the exterior angle theorem apply to triangle 1?
4. What other properties can we deduce from the right triangles in problems 2 and 3?
5. How can we use the sine and cosine laws to solve more complex triangle problems?

**Tip:** Always check if a triangle is special (e.g., isosceles, equilateral, or right-angled) as it can simplify angle and side calculations.

Solve the angles in the given triangles: 1. Find angle 'a' in an isosceles triangle with an exterior angle of 50 degrees. 2. Calculate angle 'b' in a right triangle with a 48-degree angle. 3. Determine the third angle in a right triangle with one angle of 40 degrees. 4. Solve for 'g' in a triangle with angles 'g', '2g', and '3g'.

Learn how to solve various triangle problems, including finding angles in isosceles and right triangles. Understand key concepts such as the exterior angle theorem and the sum of angles in a triangle, perfect for middle and early high school students.

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