Bisector: Using quadrilaterals

ABCD is a square.

$∢\text{ABC}=\text{?}$

Since in a square all angles are equal to 90 degrees, and BC bisects an angle, we can calculate angle ABC:

$90:2=45$

45

ABCD is a deltoid.

$∢DAC=\text{?}$

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

$BAC=CAD=2X$

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:

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

$6X+60=180$

$180-60=6X$

$120=6X$

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

$20=x$

Now we can calculate the angle DAC:

$20\times2=40$

30

ABCD rhombus

Choose the correct answer

$∢B\text{CA}=∢BAC$

ACER is a parallelogram.

$∢E=70$

AL bisects $∢\text{CAR}$

RG bisects $∢ARE$

Calculate the size of angle $∢CAL$.

35

ABCD rectangle.

DF Bisector $∢\text{CDB}$

$∢ADB=40$

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

25

ABCD is a deltoid.

$∢\text{ABC}=26$

$∢\text{CAD}=\text{?}$

64

ABCD is a quadrilateral.

AB||CD

AC||BD

CB Bisects $∢\text{ABD}$.

$∢ACD=\text{?}$

$2\alpha$