Question

1100
In the figure, ABCD is a
1 parallelogram. The diagonals
AC and BD intersect at 0; and
ZDAC = 40°, ZCAB = 35°; and
ZDOC = 110°. Calculate the
measure of ZABO, ZADC, ZACB,
and ZCBD.
30 0
Α.​

Answer 1

Answer:

<ABO= 35'

<ADC = 105 '

<ACB = 40 '

<CBD = 70 '

Step-by-step explanation:IN THIS EXPLANATION, (') IS DEGREES

In parallelogram ABCD,

<ADC+<DAB = 180'  (CORRESPONDING ANGLES IN A PARALLELOGRAM)

<ADC = 180-<DAB

           =  180 - (40+35)

             = 180-75 = 105 '

<ACB = <DAC = 40 '  (ALTERNATE INTERIOR ANGLES )

IN TRIANGLE ABO,

<AOB = <DOC (VERTICAL OPPOSITE ANGLES)

THEREFORE, <ABO= 180' - (<AOB + <OAB)  (ANGLE SUM PROPERTY)

                 = <ABO = 180 - (35+110)  = 180-145

                = <ABO = 35'

IN TRIANGLE COB,

<COB = 180 - 110 (LINEAR PAIR ) = 70'

<ACB= 40'  (ALTERNATE INTERIOR)

THEREFORE <CBD = 180' - ( 70+ 40)'

                                = 180 - 110 ' = 70'

THEREFORE, <ABO= 35'

<ADC = 105 '

<ACB = 40 '

<CBD = 70 '