Statements a and b are as given below:
a : If two lines intersect, then the vertically opposite angles are equal.
b : If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°. Then
a. Both a and b are true
b. a is true and b is false
c. a is false and b is true
d. both a and b are false
Solution:
Given two statements a and b.
We need to find which of the above statements satisfy the given options.
Considering statement a,
Consider two lines l and m which intersect each other.
Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.
Since the lines intersect, the angles x and y are vertical.
So, ∠x = ∠y
Therefore, statement a is true.
Considering statement b,
Consider two lines m and l cut by a transversal p.
From the properties of angles of a transversal on two parallel lines,
If a transversal intersects two other lines, then the sum of two interior angles on the same side of the transversal is 180°.
Therefore, statement b is equal.
✦ Try This: From the given figure, find the value of x.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 23
Statements a and b are as given below: a : If two lines intersect, then the vertically opposite angles are equal, b : If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°. Then: a. Both a and b are true, b. a is true and b is false, c. a is false and b is true, d. both a and b are false
Summary:
The given statements a and b are equal.
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