Examples with solutions for Bisector: Using quadrilaterals

Exercise #1

ABCD is a square.

ABC=? ∢\text{ABC}=\text{?}

AAABBBDDDCCC

Video Solution

Step-by-Step Solution

Due to the fact that all angles in a square are equal to 90 degrees, and BC bisects an angle, we can calculate angle ABC accordingly:

90:2=45 90:2=45

Answer

45

Exercise #2

ABCD is a deltoid.

DAC=? ∢DAC=\text{?}

AAABBBCCCDDD2x602x

Video Solution

Step-by-Step Solution

As we know that ABCD is a deltoid, and AC is the bisector of an angle and therefore:

BAC=CAD=2X BAC=CAD=2X

Now we focus on the triangle BAD and calculate the sum of the angles since we know that the sum of the angles in a triangle is 180 degrees:

2X+2X+2X+60=180 2X+2X+2X+60=180

6X+60=180 6X+60=180

18060=6X 180-60=6X

120=6X 120=6X

We divide the two sections by 6:1206=6x6 \frac{120}{6}=\frac{6x}{6}

20=x 20=x

Now we can calculate the angle DAC:

20×2=40 20\times2=40

Answer

30

Exercise #3

ABCD rhombus

Choose the correct answer

AAABBBCCCDDDαβαβ

Video Solution

Answer

BCA=BAC ∢B\text{CA}=∢BAC

Exercise #4

ABCD rectangle.

DF Bisector CDB ∢\text{CDB}

ADB=40 ∢ADB=40

Calculates the size of the angle FDC ∢\text{FDC}

AAABBBCCCDDDFFFEEEHHH40

Video Solution

Answer

25

Exercise #5

ACER is a parallelogram.

E=70 ∢E=70

AL bisects CAR ∢\text{CAR}

RG bisects ARE ∢ARE

Calculate the size of angle CAL ∢CAL .

AAACCCEEERRRGGGLLLKKK70

Video Solution

Answer

35

Exercise #6

ABCD is a deltoid.

ABC=26 ∢\text{ABC}=26

CAD=? ∢\text{CAD}=\text{?}

AAABBBDDDCCC26

Video Solution

Answer

64

Exercise #7

ABCD is a quadrilateral.

AB||CD

AC||BD

CB Bisects ABD ∢\text{ABD} .

ACD=? ∢ACD=\text{?}

αααAAABBBDDDCCC

Video Solution

Answer

2α 2\alpha