Question

A rhombus ABCD. The diogonal DB is produced to E such that BC = BE and CDE = 46. This question is taken from OXFORD SYLLABUS NEW MATHEMATICS 7TH EDITION EXCERSISE 11B Q 8. PLZ ANSWER quick as possible.

Answer 1

Answer:

angle BAD = 88

angle BCE = 23

Step-by-step explanation:

GIVEN: ABCD is rhombus

DB is produced to E

so that BC = BE

angle CDR = 46

to find angle BAD = 1

angle BCE = 2

In triangle CBD

angle BCD + angle DCB + angle CBD = 180 (angle sum property)

But angle BDC = angle CBD

(since BC = CD as side of rhombus)

46+46+angle BCD = 180

angle BCD = 88

angle BAD = BCD

(opposite side of rhombus is equal)

angle BAD = 88

we know DE is a strait line and angle DBC = 46

so,

angle DBC + angle CBE = 180

46 + angle CBE = 180

angle CBE = 180-46

= 134

In triangle BCE :

angle CBE + angle BCE + angle CEB = 180

(by angle sum property)

134 + angle BCE + angle CEB = 180

(since angle BCE = angle CEB as BC = BE - given)

134 + 2angle BCE = 180

2angle BCE = 180 - 134

angle BCE = 46/2

angle BCE = 23

so ,

angle BAD = 88

angle BAD = 88 angle BCE = 23

HENCE FOUND