Question

Abcd os a rhombus in which an altitude from d bisects ab find all angles/of the rhombus

Answer 1

Answer:

Step-by-step explanation:let @ is the angle of DAB in rohmbus

according to Rohmbus property ,

all side of rohmbus are equal .

e.g

AB = BC =CD =DA

now , Draw a rough diagram of Rohmbus ABCD

altitude from D meet in AB at M

a/c to question ,

AM = MB =1/2 AB = 1/2BC =1/2 CD =1/2AD

here ∆ ADM is right angle traingle .

where

AD is hypotenuse

DM is altitude

and AM is base

formula of cos@ =base/hypotenuse

so,

cos@ = AM/AD

from above

cos@ = 1/2AD /AD = 1/2

but we know cos60° =1/2

so, cos@ = cos 60°

@= 60° =angle DAB = angle BCD

we also know rohmbus is ||gm

so,

angle ADC +angle DAB =180°

angle ADC = 180° - 60° =120°

angle ADC = angle ABC = 120°

so,

angles of rohmbus are

60° , 120° , 60° ,120°

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