In Fig. 5.25, lines PQ and ST intersect at O. If ∠POR = 90° and x : y = 3 : 2, then z is equal to
a. 126°
b. 144°
c. 136°
d. 154°
Solution:
Given, the lines PQ and ST intersect at O.
∠POR = 90°
x : y = 3 : 2
We have to find the value of z.
We know that the sum of all angles lying on a straight line is always equal to 180 degrees.
Considering line PQ and arms OT and OR,
∠POR + ∠ROT + ∠QOT = 180°
90° + x + y = 180°
x + y = 180° - 90°
x + y = 90°
Given, x : y = 3 : 2
Let x = 3a and y = 2a
Now, 3a + 2a = 90°
5a = 90°
a = 90°/5
a = 18°
So, x = 3(18°) = 54°
y = 2(18°) = 36°
We know that the linear pair of angles is always equal to 180 degrees.
From the figure,
y + z = 180°
So, 36° + z = 180°
z = 180° - 36°
Therefore, z = 144°
✦ Try This: Pair of vertically opposite angles are always supplementary. State whether the statement is true or false
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 30
In Fig. 5.25, lines PQ and ST intersect at O. If ∠POR = 90° and x : y = 3 : 2, then z is equal to, a. 126°, b. 144°, c. 136°, d. 154°
Summary:
In Fig. 5.25, lines PQ and ST intersect at O. If ∠POR = 90° and x : y = 3 : 2, then z is equal to 144 degrees.
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