Question

Q1. Three angles of a quadrilateral are equal and the fourth angle is equal to 144º. Find each of the equal angles of
the quadrilateral.
Q2. Two consecutive angles of a parallelogram are (x + 60° and (2x + 30). What special name can you give to
this parallelogram?
Q3. If one angle of a parallelogram is 30° less than twice the smallest angle, then find the measure of each angle.
Q4. Prove that a diagonal of a parallelogram divide it into two congruent triangles.
Q5. If the diagonals of a parallelogram are equal, then show that it is a rectangle.
26. ABCD is a parallelogram and line segments AX, CY bisect the angles A and C, respectively. Show that
AX | CY.DXC
7. The diagonals of a quadrilateral ABCD are perpendicular to each other. Show that the quadrilateral formed by
joining the mid-points of its sides is a rectangle.
P.
с
OX
N
A
F
B.
In quadrilateral ABCD of the given figure. X and Y are points on diagonal AS such that AX​

Answer 1

Answer:

Thank you for these questions.......

Answer 2

Step-by-step explanation:

1. Let the three angles of quadrilateral be x°,

x+x+x+144°= 360°

3x+144°=360°

3x=360-144

3x= 216

x=72°

2. 2(x+60+2x+30)=360°

2x+120+4x+60=360°

6x+180=360

6x=180

x=30°

x+60= 30+60=90

2x+30=2×30+30=90

hence all sides are 90 degree then it is a square or rectangle.

3. smallest angle =x

one angle =x-30

2 (x+x-30)=360°

2x+2x-60= 360

4x-60= 360

4x= 420

x =105°

x-30°= 105-30=75°

hope it helps