In figure, AB || CD and ∠1 and ∠2 are in the ratio 3:2. Determine all angles from 1 to 8.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

∠1=34, ∠2=76, ∠3=34, ∠4=45, ∠5=45, ∠6=78, ∠7=56, ∠8=23

∠1=34, ∠2=44, ∠3=55, ∠4=76, ∠5=78, ∠6=87, ∠7=23, ∠8=32

∠1=90, ∠2=87, ∠3=87, ∠4=44, ∠5=32, ∠6=87, ∠7=87, ∠8=32

∠1=108, ∠2=72, ∠3=108, ∠4=72, ∠5=108, ∠6=72, ∠7=108, ∠8=72

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Concept-An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The latin word "angulus," which means "corner," is the source of the english term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
∠1 = ∠3 because they are vertically opposite angles.
∠2 = ∠4 because they are vertically opposite angles.
∠5 = ∠7 because they are vertically opposite angles.
∠6 = ∠8 because they are vertically opposite angles.
∠1 = ∠5 because they are corresponding angles.
∠2 = ∠6 because they are corresponding angles.
∠1 and ∠2 are linear pair which means the sum of these two angles is 180.
Therefore, ∠1 + ∠2 = 180
3x + 2x = 180
x = 36 Now, ∠1 = 3x = 3 36 = 108
Hence, the correct answer is 4) ∠1=108, ∠2=72, ∠3=108, ∠4=72, ∠5=108, ∠6=72, ∠7=108, ∠8=72

Watch 3-min video & get full concept clarity