Mathematics

How many pairs of adjacent angles, in all, can you name in figure?

10

SOLUTION
Let the apparently visible angles be  a, b, c & d.
Each angle has 3 adjacent angles.
The combinations are,
for a$\longrightarrow$(a,b),  (a, b+c),  (a, b+c+d) and
for b$\longrightarrow$(a,b),  (b,c),  (b, c+d) and
for c$\longrightarrow$(b,c),  (c, a+b),  (c,d) and
for d$\longrightarrow$(c,d),  (d, b+c),  (d, a+b+c) and
(a+b),  (c+d).
Omitting one of the terms which come  twice we have
(a, b+c),  (a, b+c+d),  (a,b),  (b, c+d),  (b,c)  (c, b+a),  (c,d)  (d, b+c),
(d, a+b+c),  (a+b,  c+d) .
So the total number of  the pairs of adjacent angles=10.
Ans- Option D.

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!

Single Correct Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 87

Realted Questions

Q1 Single Correct Medium
In the given figure, $PA\parallel BC\parallel DQ$ and $AB\parallel DC$. Then the values of $x$ and $y$ are respectively:
• A. $50^{0},120^{0}$
• B. $60^{0},120^{0}$
• C. $60^{0},130^{0}$
• D. $50^{0},130^{0}$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 23rd 09, 2020

Q2 Subjective Medium
Fill in the blanks
An angle which measure is $180^{o}$ is called ..

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Subjective Medium
In the below given figure, prove that $p$ $||$ $m.$

Asked in: Mathematics - Straight Lines

1 Verified Answer | Published on 17th 08, 2020

Q4 Subjective Medium
In the joining figure, name the following pairs of angles.
Adjacent angles that do not form a linear pair.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Subjective Medium
Read the following two statements which are taken as axioms:
(i) If two lines intersect each other, then the vertically opposite angles are not equal.
(ii) If a ray stands on a line, then the sum of two adjacent angles so formed is equal to $180^0$.
Is this system of axioms consistent? Justify your answer.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020