Question

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14 question

Answer 1

Answer:50°

Step-by-step explanation:

Angle AOD = 100°

WE KNOW THAT DIAGONALS OF A RECTANGLE ARE EQUAL AND BISECT EACH OTHER THUS, OD = OA

THEREFORE TRIANGLE AOD IS AN ISOSCELES TRIANGLE

AND WE ALSO KNOW THAT ANGLES OPPOSITE TO THE EQUAL SIDES ARE EQUAL,IN THIS CASE ANGLE OAD = ODA

NOW,WE KNOW SUM OF ALL ANGLES OF A TRIANGLE IS 180 IN THIS

AOD + ODA + OAD = 180

AOD + ODA + ODA = 180(WE HAVE PROVED ABOVE THAT OAD = ODA)

100 + 2(ODA) = 180

2ODA = 180 - 100 = 80

ODA = 80 ÷ 2 = 40°

ODA = OAD = 40

WE KNOW THAT EAC ANGLE OF RECTANGLE MEASURES 90

THUS ANGLE OAB = 50

SINCE WE ALSO KNOW THAT RECTANGLE IS A PARALLELOGRAM

SIDES DC AND AB ARE PARALLEL AND AC ACTS AS A TRANSVERSAL

THERE ANGLE CAB = ACD = 50(ALTERNATE INTERIOR ANGLES)

Answer 2

Angle AOD = 100°

WE KNOW THAT DIAGONALS OF A RECTANGLE ARE EQUAL AND BISECT EACH OTHER THUS, OD = OA

THEREFORE TRIANGLE AOD IS AN ISOSCELES TRIANGLE

AND WE ALSO KNOW THAT ANGLES OPPOSITE TO THE EQUAL SIDES ARE EQUAL,IN THIS CASE ANGLE OAD = ODA

NOW,WE KNOW SUM OF ALL ANGLES OF A TRIANGLE IS 180 IN THIS

AOD + ODA + OAD = 180

AOD + ODA + ODA = 180(WE HAVE PROVED ABOVE THAT OAD = ODA)

100 + 2(ODA) = 180

2ODA = 180 - 100 = 80

ODA = 80 ÷ 2 = 40°

ODA = OAD = 40

WE KNOW THAT EAC ANGLE OF RECTANGLE MEASURES 90

THUS ANGLE OAB = 50

SINCE WE ALSO KNOW THAT RECTANGLE IS A PARALLELOGRAM

SIDES DC AND AB ARE PARALLEL AND AC ACTS AS A TRANSVERSAL

THERE ANGLE CAB = ACD = 50(ALTERNATE INTERIOR ANGLES)