Triangle Angle Relationships and Theorems

This video tutorial focuses on solving various problems related to triangles, including calculating unknown angles using the angle sum property, exterior angle theorem, and mid-segment theorem. It covers basic to complex problems, such as finding angles in isosceles triangles, using algebraic expressions, and understanding linear pairs. The tutorial also explores the ratio of interior angles and provides multiple methods to solve for unknowns, enhancing problem-solving skills in geometry.

If angle A is 60 degrees and angle B is 70 degrees in a triangle, what is the measure of angle C?

• 60 degrees

• 70 degrees

• 40 degrees

• 50 degrees

In a triangle, angle A is 4x - 2, angle B is 10x, and angle C is 8x + 6. What is the value of x?

• 6

• 8

• 10

• 12

In an isosceles triangle, if angle B is 50 degrees, what is the measure of angle A?

• 65 degrees

• 70 degrees

• 60 degrees

• 50 degrees

What is the measure of angle 5 if it forms a linear pair with an angle of 40 degrees?

• 150 degrees

• 140 degrees

• 130 degrees

• 120 degrees

If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

• 90 degrees

• 80 degrees

• 70 degrees

• 60 degrees

Using the exterior angle theorem, if the remote interior angles are 40 and 55 degrees, what is the exterior angle?

• 90 degrees

• 85 degrees

• 100 degrees

• 95 degrees

In a triangle with a mid-segment, if the length of the mid-segment is 15, what is the length of the side parallel to it?

• 20

• 25

• 35

• 30

In a triangle with altitudes, if angle BAC is 50 degrees and angle ACB is 60 degrees, what is the measure of angle AFC?

• 130 degrees

• 100 degrees

• 110 degrees

• 120 degrees

If angle BCD is 12x - 4 and angle A is 4x + 2, what is the value of x?

• 1

• 7

• 3

• 5

In a triangle, if angle A is 4x + 2 and angle B is x^2 + 1, what could be the measure of angle A?

• 40 degrees

• 12 degrees

• 6 degrees

• 30 degrees