Page 153 - Math Smart - 7

d) MCD is an isosceles triangle, 3^^ BD bisect each other. So, MD = MC
The diagonals of a square
^y._^ 180°-ZC/WD divide the angles at the
corners into 45° angles.
= 180°-90°
2
_ 90!
2
= 45°

Q PQRS is a rectangle. Find the following angles.

100° ^ ^ y
a) APSR b) zlx
c) AQOR d)

X

Solution
a) PQRS is a rectangle. Each angle at the corner of a rectangle
So, ZPS/? = 90°. is a right angle.

b) QS is a straight line.
Sum of angles on a straight line is 180°.
So, ZP05= 180°-100° When two straight lines
= 80°. cut each other, the angles
opposite each other are
PR is a straight line.
equal.
So, ^x=180°-80° Sum of angles on a straight line is 180°.
= 100°. AP0Q= A SOR
APOS=AQOR
c) PR is a straight line.
Sum of angles on a straight line is 180°.
So, ^Q0/?= 180°-100= Each pair of angles are
= 80°. vertically opposite angles.
d) ^OQP is an isosceles triangle.
180°-ZOO/? other.
zx=
So, OR = OS.
= 180°-80°
2
= 100°
2
= 50°.