Question

in figure AB is parallel to CD and EF is parallel to DQ determine Angle PDQ, angle AED and angle DEF.

Answer 1

Hey Here Is Your Answer! ! ! !

Angle CDP = angle AED ( Corresponding angle)
SO angle AED = 34 -(i)


Now,
Angle AED + Angle DEF + Angle FEB = 180 ( angles on straight line )
34 + Angle DEF + 78 = 180 ( Angle AED = 34 is proved above & Angle FEB = 78 given)
Angle DEF + 112 = 180
Angle DEF = 180-112
Angle DEF = 68
So Angle DEF = 68

Angle DEF = Angle PDQ ( Corresponding angle)
So Angle PDQ = 68



I HOPE ITS HELPFULL FOR YOU.

IF IT HELPFULL FOR YOU THAN MARK AS A BRAINLIST.

THANK YOU.

☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺

Answer 2

Answer:

<PDQ = 68°, <AED = 34°, < DEF = 68°

Step-by-step explanation:

<PDC = <DEA = 34°

(corresponding angles)

<AED + <DEC + <BEF = 180°  ( straight line angle)

34° + <DEC + 78° = 180°

112°+ <DEC = 180°

<DEC = 180° - 112° = 68°

<DEC = <PDQ = 68°

(corresponding angles)

Thus, <PDQ = 68°, <AED = 34°, < DEF = 68°

Parallel lines

Two lines are said to be parallel when they do not intersect each other.

Transversals

When a line intersects two lines at distinct points, it is called a transversal.

Corresponding Angles:

Corresponding angles are the angles that are formed in matching corners or corresponding corners with the transversal when two parallel lines and the transversal.

Alternate interior angles:

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.

Alternate exterior angles:

Alternate exterior angles are the pair of angles that are formed on the outer side of two lines but on the opposite side of the transversal.