Lines and Angles Test

Result

Lines and Angles Test - 36

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following pairs represents pairof corresponding angles.

A
$$\angle a$$ and $$\angle d$$

B
$$\angle a$$ and $$\angle e$$

C
$$\angle \mathrm { d }$$ and $$\angle i$$

D
$$\angle \mathrm { c }$$ and $$\angle \mathrm { h }$$

Solution
Question 2
1 / -0

If the supplement of an angle is $$\dfrac { 5 }{ 2 } $$ times the complement of the same angle, find the supplementary angle.

A
$${ 150 }^{ \circ }$$

B
$${ 60 }^{ \circ }$$

C
$${ 30 }^{ \circ }$$

D
$${ 120 }^{ \circ }$$
Question 3
1 / -0

In triangle, three angles are $$x , x + 10 ^ { \circ } + x + 20 ^ { \circ }$$ then the biggest is

A
$$70 ^ { \circ }$$

B
$$80 ^ { \circ }$$

C
$$90 ^ { \circ }$$

D
none

Solution
Question 4
1 / -0

Find the lettered angle :

A
$$110^{\circ}$$

B
$$70^{\circ}$$

C
$$30^{\circ}$$

D
$$90^{\circ}$$

Solution
Question 5
1 / -0

If the angles of triangle are in the ratio $$1:4:7$$, then the value of the largest angle is :

A
$$135^{\circ}$$

B
$$84^{\circ}$$

C
$$105^{\circ}$$

D
none of these

Solution
Question 6
1 / -0

The complementary angle of $$75^{\circ}$$ is _______.

A
$$75^{\circ}$$

B
$$105^{\circ}$$

C
$$15^{\circ}$$

D
$$25^{\circ}$$

Solution

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

Given, measure of one complementary angle is $$75^o.$$

$$\Rightarrow$$ Measure of other complementary angle $$=90^o-75^o$$ $$=15^o.$$

$$\therefore$$ Measure of a complementary angle of $$ 75^{o}=15^o$$.
Hence, option $$C$$ is correct.
Question 7
1 / -0

In the figure below, $$AA'$$ is parallel to $$CC'$$. The measure $$w$$ of $$\angle A'AB$$ is equal to $$135^\circ$$ and the measure $$z$$ of $$\angle C'CB$$ is equal to $$147^\circ$$. Find $$\angle ABC$$.

A
$$100^\circ$$

B
$$78^\circ$$

C
$$80^\circ$$

D
$$110^\circ$$

Solution

Draw $$BB'$$ parallel to $$AA'$$ and $$CC'$$as shown in the figure below.

Note that angle $$ABC$$ is given by
$$\angle ABC = \angle ABB' + \angle CBB' $$

$$\angle w'$$ and $$\angle ABB'$$ are alternate interior angles and their measure are equal.
$$\angle ABB' = \angle w' $$

$$\angle z'$$ and $$\angle CBB'$$ are alternate interior angles and their sizes are equal.
$$\angle CBB' = \angle z'$$

Angles $$w$$ and $$w'$$ are supplementary which gives
$$w' = 180^\circ - w $$
$$= 180^\circ - 135^\circ $$
$$= 45^\circ$$

Angles $$z$$ and $$z'$$ are also supplementary which gives
$$z' = 180^\circ - z $$
$$= 180^\circ - 147^\circ $$
$$= 33^\circ$$
We now substitute $$\angle ABB'$$ by $$w'$$ and $$\angle CBB'$$ by $$z'$$ in $$\angle ABC = \angle ABB' + \angle CBB'$$ found above.
$$\angle ABC = w' + z' $$
$$= 45^\circ + 33^\circ$$
$$ = 78^\circ$$
Question 8
1 / -0

Complement of $$60^o$$ is?

A
$$30^o$$

B
$$130^o$$

C
$$120^o$$

D
$$90^o$$

Solution

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

Given, measure of one complementary angle is $$60^o.$$

$$\Rightarrow$$ Measure of other complementary angle $$=90^o-60^o$$ $$=30^o.$$

$$\therefore$$ Measure of a complementary angle of $$ 60^{o}=30^o$$.
Hence, option $$A$$ is correct.
Question 9
1 / -0

Mark the correct alternative of the following.
An angle of measure $$140^o$$ is?

A
An acute angle

B
An obtuse angle

C
A straight angle

D
A complete angle

Solution

An angle that measures $$<180^o$$ but $$>90^o$$ is called an obtuse angle.
Here it is given $$140^o$$, so it is an obtuse angle.
Question 10
1 / -0

Two supplementary angles are in the ratio $$3:2$$. The smaller angle measures?

A
$$108^o$$

B
$$81^o$$

C
$$72^o$$

D
$$68^o$$

Solution

Given two supplementary angles are in the ratio $$3:2$$.
Let the measurement of the angles be $$3x$$ and $$2x$$.
Two angles are said to be supplementary if they sum upto $$180^o$$.
Then we have,
$$3x+2x=180^{o}$$
$$5x=180^o$$
or, $$x=36^o$$.
So the smaller angle is $$36^o\times 2=72^o$$.