Question

In the figure,ABCD is a rhombus. What is the measure of ABD

Answer 1

Answer:

MATHS

In the given figure, ABCD is a rhombus and ∠ABD=50°

Find :

(i) ∠CAB

(ii) ∠BCD

(iii) ∠ADC

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°