Tag: complementary angle, supplementary angles and adjcent angles

Questions Related to complementary angle, supplementary angles and adjcent angles

In $\Delta ABC$ and $\Delta DEF$, we have $\dfrac {AB}{DE}=\dfrac {BC}{FD}$. Triangles ABC and DEF will be similar if :

maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

  1. $\angle A = \angle D$

  2. $\angle A = \angle F$

  3. $\angle B = \angle E$

  4. $\angle B = \angle D$

Show answer
Correct Option: D

Using ruler and compasses only, construct a triangle POR such that $\angle P = 120^{\circ}$, PO = 5 cm PR = 6 cm.In the same figure, find a point which is equidistant from its sides. Name this point With this point as centre draw a circle touching all the sides of the triangle.

maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

  1. Circumcentre

  2. Incentre

  3. Mid point

  4. Data insufficient

Show answer
Correct Option: B
Explanation:

(I) We draw a triangle POR with $\quad \angle RPO={ 120 }^{ O }.\quad $

(II) OI & OR are the angular bisectors of $\quad \angle RPO\quad & \angle ROP\quad $
The bisectors intersect at I.
(i) IM & IN  are drawn perpendiculars from i to PR & PO respectively. 
 (iii) The circle which touches the sides of the triangle POR.
has the radius  IM=IN.
Justification-
Between $\quad \Delta IPM\quad & \quad \Delta IPN,\ \angle IMP={ 90 }^{ o }=\angle INP,\ \angle IPM=\angle IPN\quad $
So the third angles  $\quad \angle PIN=\angle PIM\quad $
Also the side IP is common.
So, by ASA rule, $\quad \Delta IPM\equiv \Delta IPN.\quad $  
i.e IM=IN.
Similarly, by considering the triangles INO & ISO it can be shown that
IN=IS.
So IM=IN=IS.
i.e the circle with centre I touches the sides of the given triangle.
So  I is the INCENTRE of the triangle POR.
Ans- Option B.

The measure of the trisected angle of $\displaystyle 162^{\circ}$ is:

maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

  1. $\displaystyle 54^{\circ}$

  2. $\displaystyle 81^{\circ}$

  3. $\displaystyle 162^{\circ}$

  4. $\displaystyle 90^{\circ}$

Show answer
Correct Option: A
Explanation:

Trisected angle $\displaystyle =\frac{162^{\circ}}{3}=54^{\circ}$

The difference between two angles is $19$$\displaystyle ^{o}$ and their sum is $\displaystyle \frac{890}{9}^o$. Find the greater angle.

maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

  1. $63^o$

  2. $35^o$

  3. $27^o$

  4. $59^o$

Show answer
Correct Option: D
Explanation:
Let the two angles be $a$ and $b$

Then, 
$a  - b = 19$

and, $a + b = \dfrac{890}{9}$

Adding the two equations,

$2a = \dfrac{890 + 19\times 9}{9}$

$2a = \dfrac{1061}{9}$

Thus, $a = \dfrac{1061}{18}$

$a \approx 59^{\circ}$

If two angles of a triangle are acute angles, the third angle:

maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

  1. is less than the sum of the two angles

  2. is an acute angle

  3. is the largest angle of the triangle

  4. may be an obtuse angle

Show answer
Correct Option: D
Explanation:
For a triangle $ABC$, sum of angles is $180^0$
Two angles are given as acute, $\angle A, \angle B < 90^0$
$\angle A = 90^0 - x$
$\angle B = 90^0 - y$
where, $x,y < 90^0$
$\therefore \angle A + \angle B+ \angle C = 180^0$
$\Rightarrow \angle C = x+y $
$x+y$ can be $>90^0$ or $<90^0$
So, it may be obtuse or acute.
Hence, option D.

An angle which measures $\displaystyle 0^{o}$ is called:

maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

  1. obtuse angle

  2. straight angle

  3. zero angle

  4. right angle

Show answer
Correct Option: C
Explanation:

An angle which measure $0^0$ is called zero angle.

An angle which measure more than $0^o$ and less than $90^o$ is an acute angle.
An angle which measures $90^o$ is called a right angle.
An angle which measure more than $90^o$ and less than $180^o$ is an obtuse angle.

Hence, the answer is zero angle.

Find the supplement  of the following angle.
$40^{\circ}$

maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

  1. $140$

  2. $40$

  3. $10$

  4. None of these

Show answer
Correct Option: A
Explanation:

We know that the supplement angle

$=180^0-\theta$

So,
The supplement angle of $40^0$ will be
$=180^0-40^0=140^0$ 

Hence, this is the answer.

Two triangles are similar, if their corresponding angles are ________.

maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

  1. Proportional

  2. Equal

  3. A & B

  4. None of the above

Show answer
Correct Option: B
Explanation:

Two triangles are similar, if their corresponding angles are equal.

(Two triangles are similar, if their corresponding angles are equal and corresponding sides are proportional.)