Question

# In quadrilateral $$ABCD$$, if $$\angle A = 60^{\circ}$$ and $$\angle B : \angle C : \angle D = 2 : 3 : 7$$, then find $$\angle D$$.

A
175
B
135
C
150
D
120

Solution

## The correct option is D $$175^{\circ}$$In quadrilateral $$ABCD$$, $$\angle A$$ = $$60^\circ$$ and $$\angle B: \angle C: \angle D = 2 : 3 : 7$$        [Given].Let $$\angle B, \angle C, \angle D$$ are $$2x^\circ$$ , $$3x^\circ$$ and $$7x^\circ$$.$$\Rightarrow$$  $$\angle A+ \angle B+ \angle C + \angle D$$=$$360^\circ$$    [Sum of all angles of quadrilateral is $$360$$$$^\circ$$]$$\Rightarrow$$  $$60^\circ + 2x^\circ+ 3x^\circ +7x^\circ$$ = $$360^\circ$$$$\Rightarrow$$  $$12x^\circ$$ = $$360^\circ - 60^\circ$$$$\Rightarrow$$  $$x^\circ$$ = $$\dfrac {300^\circ}{12}$$$$\Rightarrow$$  $$x^\circ$$ = $$25^\circ$$.Now, $$\angle D$$=$$7x^\circ$$.Substitute value of $$x$$ we get,$$\Rightarrow$$  $$\angle D$$=$$7\times 25^o$$$$\therefore$$  $$\angle D = 175^\circ$$.Hence, option $$A$$ is correct.Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More