Exploring Angle Addition and Bisectors

This video tutorial covers the angle addition postulate and angle bisectors. It begins with an introduction to the angle addition postulate, explaining how it is used to find unknown angle measures. The tutorial then demonstrates applying this postulate through examples. Following this, the concept of angle bisectors is introduced, highlighting their properties and how they divide angles into congruent parts. The video concludes with problem-solving examples using angle bisectors and algebra to find unknown angle measures.

What are the two main concepts covered in this lesson?

• Segment addition postulate and angle bisectors

• Segment subtraction postulate and angle bisectors

• Angle addition postulate and angle bisectors

• Angle subtraction postulate and angle bisectors

According to the segment addition postulate, if a point Z is placed between points R and S on a line segment, what is true?

• The distance from R to S is equal to the distance from R to Z plus the distance from Z to S

• The distance from R to S is equal to the distance from R to Z minus the distance from Z to S

• The distance from R to S is equal to the distance from R to Z divided by the distance from Z to S

• The distance from R to S is equal to the distance from R to Z times the distance from Z to S

In the angle addition postulate, where is the point placed?

• On the exterior of the angle

• On the vertex of the angle

• In the interior of the angle

• On the bisector of the angle

What is the measure of angle ABC if angle ABP is 85° and angle PBC is 39°?

• 124°

• 39°

• 85°

• 100°

If the measure of angle M is 124° and it is divided into two smaller angles by a ray, what is the sum of the measures of the two smaller angles?

• 62°

• 248°

• 124°

• 100°

What does an angle bisector do?

• Divides a segment into two congruent segments

• Divides an angle into two unequal angles

• Divides a segment into two unequal segments

• Divides an angle into two congruent angles

If an angle bisector divides angle ABC into two congruent angles, and one of the smaller angles measures 37°, what is the measure of angle ABC?

• 74°

• 90°

• 37°

• 54°

Given that angle ABC is bisected by ray BD, if angle ABD is 4x + 28° and angle ABC is 12x + 16°, what is the value of x?

• 10

• 12

• 8

• 14

If the measure of angle ABD is 4x + 28° and x is found to be 10, what is the measure of angle ABD?

• 68°

• 78°

• 88°

• 98°

How can you verify the measures of angles found using the angle addition postulate?

• By ensuring the sum of the smaller angles equals the larger angle

• By ensuring the quotient of the smaller angles equals the larger angle

• By ensuring the product of the smaller angles equals the larger angle

• By ensuring the difference of the smaller angles equals the larger angle