Question

In the below given figure, ABCD is a rhombus and ∠ABD = 50॰. Find (i) ∠CAB (ii) ∠BCD (iii)∠ADC (iv) ∠BDC​

Answer 1

ANSWER

From the figure it is given that, ABCD is a rhombus∠ABD=50

(i) Consider the △AOB, We know that, sum of measures of interior angles of triangle is equal to 180

∠OAB+∠BOA+∠ABO=180

∠OAB+90

+50

=180

By transposing we get,

∠OAB+140

=180

∠OAB=180

−140

∠OAB=40

Therefore, ∠CAB=40

(ii) ∠BCD=2∠ACD

=2×40

=80

(iii) Then, ∠ADC=2∠BDC

∠ABD=∠BDC because alternate angles are equal

=2×50

=100