Proposed Problem

Click the figure below to see the complete problem 382 about Concave Quadrilateral, Angle Bisectors, Angles.

See more:

Complete Geometry Problem 382

Level: High School, SAT Prep

## Saturday, October 31, 2009

### Problem 382. Concave Quadrilateral, Angle Bisectors, Angles

Labels:
angle,
angle bisector,
concave,
quadrilateral,
triangle

Subscribe to:
Post Comments (Atom)

Extend CE & CD to meet AB in F & G resply.

ReplyDeleteangle GFC= α + C/2 and angle x = angle GFC + A/2

Hence, x = α + C/2 + A/2 or 2(x- α) = A + C

Likewise, angle AGC = α + C and β = ang. AGC + A or β = α + C + A Or β = α + 2(x- α) = 2x – α or x = (α+ β)/2

Ajit

Let alpha=a, beta=b.

ReplyDeleteLet measure angle EAD=z and measure angle ECD=w.

ABCD is a concave quadrilateral,

hence, b = a + 2z + 2w...(1)

ABCE is a concave quadrilateral,

hence, x = z+ w + a...(2)

(a + b)/2=(a+a+2z+2w)/2...(by (1))

=2(a+z+w+)/2

=a+z+w

=x...(by (2))