Question

1. for each triangle, check all that apply.

triangle a
triangle b
triangle c
triangle d
triangles a, b, c, d images
scalene
isosceles
equilateral
scalene
isosceles
equilateral
scalene
isosceles
equilateral
scalene
isosceles
equilateral

1. find the value of x.

triangle with angles 72°, 57°, x° image

1. find the value of x.

triangle with angles 32°, 111° and exterior angle x° image

1. write an equation to find x. then find the degree measure of each angle.

triangle kml with angles (7x - 8)°, (2x - 2)°, x° image
m∠k = ____ m∠l = __ m∠m = ____

Explanation:

Problem 1: Classify Triangles

Triangle A:

• Sides: 4, 8, 8. Two sides equal, so Isosceles (not Scalene, not Equilateral).

Triangle B:

• Angles: \(60^\circ, 60^\circ, 60^\circ\) (all angles equal, so all sides equal). Thus Isosceles (and Equilateral, since Equilateral is a special case of Isosceles).

Triangle C:

• Angles: \(75^\circ, 60^\circ, 45^\circ\) (all angles different, so all sides different). Thus Scalene (not Isosceles/Equilateral).

Triangle D:

• Sides: 11, 7, 5 (all sides different). Thus Scalene (not Isosceles/Equilateral).

Problem 2: Find \(x\) (Triangle Angle Sum)

Step1: Recall triangle angle sum (\(180^\circ\))

\(x + 72 + 57 = 180\)

Step2: Solve for \(x\)

\(x = 180 - 72 - 57 = 51\)

Step1: Find the third interior angle

Third angle \(= 180 - 32 - 111 = 37^\circ\)

Step2: Use exterior angle theorem (exterior angle = sum of two remote interior angles)

\(x = 32 + 111 = 143\) (or \(x = 180 - 37 = 143\))

Step1: Triangle angle sum equation

\((7x - 8) + (2x - 2) + x = 180\)

Step2: Simplify and solve for \(x\)

\(10x - 10 = 180\)
\(10x = 190\)
\(x = 19\)

Step3: Calculate each angle

• \(m\angle K = 7(19) - 8 = 125^\circ\)
• \(m\angle L = 2(19) - 2 = 36^\circ\)
• \(m\angle M = 19^\circ\)

Answer:

\(x = 51\)

Problem 3: Find \(x\) (Exterior Angle Theorem)