Examples with solutions for Bisector: Angle bisector

Exercise #1

BD is a bisector.

What is the size of angle ABC?

656565AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Since we are given that the value of angle DBC is 65 degrees, and we know that the angle bisector divides angle ABC into two equal angles, we can calculate the value of angle ABC:

65+65=130 65+65=130

Answer

130

Exercise #2

Calculate angle α \alpha given that it is a bisector.

ααα606060AAAaaa

Video Solution

Step-by-Step Solution

Since an angle bisector divides the angle into two equal angles, and we are given that one angle is equal to 60 degrees. Angle α \alpha is also equal to 60 degrees

Answer

60

Exercise #3

ABD=90 ∢\text{ABD}=90

CB bisects ABD \sphericalangle\text{ABD} .

CBD=α \sphericalangle\text{CBD}=\alpha

Calculate the size of ABC ∢ABC .

AAABBBDDDCCCα

Video Solution

Answer

45

Exercise #4

ABD=15 ∢\text{ABD}=15

BD bisects the angle.

Calculate the size of ABC ∢\text{ABC} .

AAABBBCCCDDD15

Video Solution

Answer

30

Exercise #5

Given:

ABC=90 ∢\text{ABC}=90

DBC=45 ∢DBC=45

Is BD a bisector?

AAABBBCCCDDD45

Video Solution

Answer

Yes

Exercise #6

ABC=120 ∢ABC=120

ABD=60 ∢ABD=60

Which of the following are true?

AAABBBCCCDDD60120

Video Solution

Answer

BD bisects ABC ∢ABC .

Exercise #7

Calculate the size of angle α \alpha given that it is a bisector.αααaaa

Video Solution

Answer

45

Exercise #8

BO bisects ABD ∢ABD .

ABD=85 ∢\text{ABD}=85

Calculate the size of

ABO. \sphericalangle ABO\text{.} 85°85°85°AAACCCBBBOOODDD

Video Solution

Answer

42.5

Exercise #9

DBC=90° ∢DBC=90°

BE cross DBA ∢\text{DBA}

Find the value α \alpha

AAABBBCCCDDDEEEα

Video Solution

Answer

45

Exercise #10

The triangle ABC is shown below.

CD bisects C.

Angle C equals 122 degrees.

Calculate angle ACD ∢\text{ACD} .AAABBBCCCDDD

Video Solution

Answer

61°

Exercise #11

Shown below is the triangle ABC.

Angle A is 80 degrees and is intersected by AD.

Calculate angle DAB.

AAABBBCCCDDD

Video Solution

Answer

40°

Exercise #12

The triangle ABC is shown below.

BD bisects B.

Angle B is 66 degrees.

Calculate the angle DBC ∢\text{DBC} AAABBBCCCDDD

Video Solution

Answer

33°

Exercise #13

a is a bisector.

BAC=80° ∢BAC = 80°

Calculate angle α \alpha .

αααaaaAAABBBCCC

Video Solution

Answer

40

Exercise #14

ABC =130 ∢ABC\text{ }=130

Given that a is a bisector, calculate angle α \alpha .

αααaaaAAABBBCCC

Video Solution

Answer

65

Exercise #15

What is the size of angle ABC given that BD is a bisector?

AAABBBCCCDDD40

Video Solution

Answer

80

Exercise #16

BE bisects FBD ∢\text{FBD} .

FBE=25 ∢\text{FBE}=25

Calculate the size of EBD ∢\text{EBD} .

AAACCCBBBFFFEEEDDD25

Video Solution

Answer

25

Exercise #17

BD bisects ABC ∢\text{ABC} .

EBC=α ∢EBC=\alpha

DBE=30 ∢DBE=30

Calculate the size of ABD ∢\text{ABD} .

αααAAABBBCCCDDDEEE30

Video Solution

Answer

α+30 \alpha+30

Exercise #18

AFB=60 ∢\text{AFB}=60

AFE=120 ∢\text{AFE}=120

EFD=80 ∢EFD=80

FC bisects DFB ∢DFB .

Calculate the size of angle DFC ∢\text{DFC}

EEEBBBAAACCCDDD6012080F

Video Solution

Answer

50

Exercise #19

Which line segment(s) are bisectors?

120°120°120°120°120°120°AAABBBCCCDDD

Video Solution

Answer

All of the above.

Exercise #20

Given:

ABC=90 ∢ABC=90

ABD=45 ∢ABD=45

EBC=22.5 ∢EBC=22.5

Choose sides that are bisectors

AAABBBCCCDDDEEE22.545

Video Solution

Answer

Answers a + b