Question

7. In a pentagon ABCDE, AB is parallel to DC
and angleA: angleE: angleD = 3: 4: 5. Find angle E.​

Answer 1

Answer:

In a pentagon ABCDE, AB is parallel to DC and ∠A:∠E:∠D=3:4:5

So, ∠B+∠C=180° (Sum of interior angles on the same side of transversal are supplementary.)

Let ∠A=3x,∠E=4x,∠D=5x

Sum of all interior angles of pentagon = 180°

(n−2)=180°

(5−2)=540°

Now,

∠B+∠C+∠A+∠E+∠D=540°

=>180° +3x+4x+5x=540°

=>12x=360°

=>x=30°

∠E=4x=4×30° =120°

Hope this is helpful for you.