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### Question 2: Determine the value of the pronumerals in each of the following polygons.

#### a. Triangle with angles 95°, 130°, and \( a \)
- We know that the sum of angles in a triangle is always 180°.
  
\[
a + 95^\circ + 130^\circ = 180^\circ
\]
\[
a = 180^\circ - 95^\circ - 130^\circ = -45^\circ
\]

Since the sum exceeds 180°, this might indicate a non-triangle. Ensure correct geometry assumptions in such cases.

#### b. Triangle with angles 40°, 70°, and \( d \)
Using the angle sum property of a triangle:
\[
d + 40^\circ + 70^\circ = 180^\circ
\]
\[
d = 180^\circ - 40^\circ - 70^\circ = 70^\circ
\]

#### c. Triangle with angles 20°, 90°, and \( i \)
This is a right-angled triangle (90°):
\[
i + 20^\circ + 90^\circ = 180^\circ
\]
\[
i = 180^\circ - 20^\circ - 90^\circ = 70^\circ
\]

#### d. Angles \( l \), \( k \), \( j \), and \( m \)
This forms a quadrilateral. The sum of angles in a quadrilateral is 360°. Given:
\[
50^\circ + j + l + m = 360^\circ
\]

### Question 3: Evaluate the pronumerals and determine the size of the interior angles for triangles.

#### a. Isosceles triangle with \( y \) and angle 55°
In an isosceles triangle, two angles are equal. Let the equal angles be \( y \):
\[
2y + 55^\circ = 180^\circ
\]
\[
2y = 180^\circ - 55^\circ = 125^\circ
\]
\[
y = \frac{125^\circ}{2} = 62.5^\circ
\]

#### b. Triangle with 15° and 160° angles
\[
x + 15^\circ + 160^\circ = 180^\circ
\]
\[
x = 180^\circ - 15^\circ - 160^\circ = 5^\circ
\]

#### c. Equilateral triangle with angles \( n \)
All angles are equal:
\[
3n = 180^\circ
\]
\[
n = \frac{180^\circ}{3} = 60^\circ
\]

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Would you like further explanation on any part of this? Here are 5 related questions you can consider:

1. What is the angle sum property of polygons?
2. How do exterior angles relate to interior angles in polygons?
3. How can you identify a right triangle using angles?
4. What makes an isosceles triangle unique in terms of its angles?
5. How can we find the exterior angles of a triangle?

**Tip**: Always remember, the sum of the interior angles of a triangle is always 180°.

Determine the value of the pronumeral in each of the following polygons.

This problem involves determining the value of pronumerals in various polygons, including triangles and quadrilaterals. Concepts covered include the triangle angle sum property, quadrilateral angle sum, and working with isosceles and equilateral triangles. Suitable for students in Grades 7-9.

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