Lines and Angles Test

Result

Lines and Angles Test - 33

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Weekly Quiz Competition

Question 1
1 / -0

The angles of a triangle are in the ratio of $$3:5:7.$$ What is the measure of the largest interior angle of the triangle?

A
$$18^{o}$$

B
$$48^{o}$$

C
$$84^{o}$$

D
$$96^{o}$$

Solution

By angle sum property, the sum of angles is $$180^o$$.
Let $$3x, 5x$$ and $$7x$$ be the three angles of the triangle.
So,
$$3x + 5x + 7x = 180^{o}$$
$$15x = 180^{o}$$
$$x = 12^{o}$$

Hence, Largest interior angle $$= 7 \times 12^{o} = 84^{o}$$
Question 2
1 / -0

In $$\triangle ABC$$, if $$\angle B = \angle C = 45^{\circ}$$, which of the following is correct?

A
$$\angle A= 60°$$

B
$$\angle A= 70°$$

C
$$\angle A= 80°$$

D
$$\angle A= 90°$$

Solution

As $$\angle B=\angle C=45^{\circ}$$ and by angle sum property, the sum of angles is $$180^o$$.
$$\therefore \angle A+\angle B+\angle C=180^{\circ}$$
$$\Rightarrow \boxed{\angle A=90^{\circ}}$$
Question 3
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Which of the following are complementary angles?

A
$$71^o$$ and $$19^o$$

B
$$18^o$$ and $$180$$

C
$$90^o$$ and $$90^o$$

D
$$90^o$$ and $$45^o$$

E
$$15^o$$ and $$30^o$$

Solution
Question 4
1 / -0

What is the measure of angle B in the following figure if angle A measures $$135^o$$?

A
$$40^o$$

B
$$45^o$$

C
$$50^o$$

D
$$135^o$$

Solution
Question 5
1 / -0

In the adjacent figure PQ || ST, $$\angle PQR = 110^o$$ and $$\angle RST = 130^o$$, find $$\angle QRS$$.

A
$$30^o$$

B
$$130^o$$

C
$$60^o$$

D
$$160^o$$

Solution

Draw a line $$XY$$ parallel to $${{PQ}}\parallel {{ST}}$$.
It is known that the sum of interior angles on the same side of the transversal is $$180^\circ $$.
So, $$\angle {{PQR}} + \angle {{QRX}} = 180^\circ $$
$$110^\circ + \angle {{QRX}} = 180^\circ $$
$$\angle {{QRX}} = 70^\circ $$
Similarly,
$$\angle {{RST}} + \angle {{SRY}} = 180^\circ $$
$$130^\circ + \angle {{SRY}} = 180^\circ $$
$$\angle {{SRY}} = 50^\circ $$
Now, by property of linear pair,
$$\angle {{QRX}} + \angle {{QRS}} + \angle {{SRY}} = 180^\circ $$
$$70^\circ + \angle {{QRS}} + 50^\circ = 180^\circ $$
$$\angle {{QRS}} = 60^\circ $$
Question 6
1 / -0

Find the complement of each of the following angles $$24^{\circ}$$.

A
$$66^{\circ}$$

B
$$156^{\circ}$$

C
$$36^{\circ}$$

D
None of these

Solution

We know, two angles are complementary when they add up to $$90^o.$$
Given, measure of one complementary angle is $$24^o.$$
$$\Rightarrow$$ Measure of other complementary angle $$=90^o-24^o$$ $$=66^o.$$
$$\therefore$$ Measure of a complementary angle of $$ 24^{o}=66^o$$.
Therefore, option $$A$$ is correct.
Question 7
1 / -0

Find the complement of each of the following angles $$20^{\circ}$$.

A
$$70^{\circ}$$

B
$$60^{\circ}$$

C
$$110^{\circ}$$

D
None of these

Solution

We know, two angles are complementary when they add up to $$90^o.$$
Given, measure of one complementary angle is $$20^o.$$
$$\Rightarrow$$ Measure of other complementary angle $$=90^o-20^o$$ $$=70^o.$$
$$\therefore$$ Measure of a complementary angle of $$ 20^{o}=70^o$$.
Therefore, option $$A$$ is correct.
Question 8
1 / -0

Find the complement of each of the following angles $$48^{\circ}$$.

A
$$42^{\circ}$$

B
$$52^{\circ}$$

C
$$132^{\circ}$$

D
None of these

Solution

We know, two angles are complementary when they add up to $$90^o.$$

Given, measure of one complementary angle is $$48^o.$$

$$\Rightarrow$$ Measure of other complementary angle $$=90^o-48^o$$ $$=42^o.$$

$$\therefore$$ Measure of a complementary angle of $$ 48^{o}=42^o$$.
Therefore, option $$A$$ is correct.
Question 9
1 / -0

Find the complement of each of the following angles $$35^{\circ}$$.

A
$$55^{\circ}$$

B
$$145^{\circ}$$

C
$$35^{\circ}$$

D
None of these

Solution

We know, two angles are complementary when they add up to $$90^o.$$
Given, measure of one complementary angle is $$35^o.$$
$$\Rightarrow$$ Measure of other complementary angle $$=90^o-35^o$$ $$=55^o.$$
$$\therefore$$ Measure of a complementary angle of $$ 35^{o}=55^o$$.
Therefore, option $$A$$ is correct.
Question 10
1 / -0

Find the complement of the following angles:
$$63^{\circ}$$.

A
$$27^{\circ}$$

B
$$54^{\circ}$$

C
$$117^{\circ}$$

D
None of these

Solution

We know, two angles are complementary when their sum is equal to $$90^o.$$
Given, measure of one angle is $$63^o.$$
$$\Rightarrow$$ Measure of its complementary angle $$=90^o-63^o$$ $$=27^o.$$
$$\therefore$$ Measure of complementary angle of $$ 63^{o}=27^o$$.
Option $$A$$ is correct.