Construction of Standard Angles

Q.

Question 8

Draw an angle of ${70}^{\circ }$. Make a copy of it using only a straight edge and compasses.

Q. To construct an angle of ${60}^{\circ }$

Steps of construction are:
Step 1: Draw a ray AB
Step 2 will be:

1. Taking D as center and any radius, draw an arc intersecting the previous arc at E.
2. Taking A as centre and any convenient radius, draw an arc intersecting ray AB at a point D.
3. Using protractor, draw an angle ${60}^{\circ }$.
4. Taking D as center and same radius, draw an arc intersecting the previous arc at E.

Q.

Draw a line $l$ and a point $X$ on it. Through $X$, draw a line segment $\overline{XY}$ perpendicular to $l$. Now draw a perpendicular to $\overline{XY}$ to $Y$. (use ruler and compasses)

Q. Question 1
Draw an angle of ${110}^{\circ }$ with the help of a protractor and bisect it. Measure each angle.

Q. Arrange the steps of construction of ${30}^{\circ }$ angle in a proper sequential order.
Step 1 :
Construct a ${60}^{\circ }$ angle.
Step 2:
Draw a bisector for ${60}^{\circ }$ angle to get ${30}^{\circ }$ angle.

1. 1, 2
2. 2, 1
3. Steps may be followed in any order
4. Given steps are incorrect

Q. Question 4 (ii)
Construct the following angles and verify by measuring them by a protractor:
(ii) ${105}^{\circ }$

Q.

Is it possible to construct a unique quadrilateral ABCD with AB = 4 cm, AD = 6 cm, $\angle$ABC = ${60}^{\circ }$, $\angle$DAB = ${75}^{\circ }$,

$\angle$ADC = ${85}^{\circ }$? If yes, construct it and find $\angle$BCD.

1. No, it is impossible

2. yes,

3. yes,

4. yes,

Q.

During construction of a ${60}^{\circ }$ angle, minimum 3 arcs need to be drawn.

1. True

2. False

Q.

The steps to construct ${60}^{\circ }$ angle is given below. Arrange these steps in the correct sequence.

1. Taking O as centre, draw an arc of any size to cut OA at B.

2. Draw a line segment OA of any suitable length.

3. Join OC and produce it to any point D.

4. With B as centre draw another arc of the same size to cut the previous arc at C.

1. 2, 1, 4, 3

2. 2, 1, 3, 4

3. 1, 2, 3, 4

4. 4, 3, 1, 2

Q. Suppose $Q$ is a point on the circle with centre $P$ and radius $1$, as shown in the figure; $R$ is a point outside the circle such that $QR=1$ and $\angle QRP=2^{\circ }$. Let $S$ be the point where the segment $RP$ intersects the given circle. Then measure of $\angle RQS$ equals:

1. ${86}^{\circ }$
2. ${87}^{\circ }$
3. ${88}^{\circ }$
4. ${89}^{\circ }$

Q.

Continuing with the previous question, what angle do we have at the end of four arcs?

With B as the centre and any radius more than half of AB, draw another arc as shown. This is the third arc. With A as the centre and the same radius as above, cut the previously drawn arc in Y. This would the fourth arc. Join PY.

What is ∠YPA?

1. ${30}^{\circ }$

2. ${90}^{\circ }$
3. ${180}^{\circ }$
4. ${60}^{\circ }$

Q.

In the given figure if $\angle$ BAC = ${60}^{\circ }$, AB = AC = 6cm then find the length of BC.

1. 6

2. 12

3. 10

4. 3

Q.

In the process of construction of an angle with P as the centre and any radius, draw an arc as shown, which cuts in A. This is the first arc. With A as centre and the same radius, cut this arc in B. This would be the second arc. What will be the value of $\angle BPA$?

1. $\angle$ BPA = ${30}^{\circ }$

2. $\angle$ BPA = ${60}^{\circ }$

3. $\angle$ BPA = ${90}^{\circ }$

4. $\angle$ BPA = ${180}^{\circ }$

Q.

Observe the given construction, if $\angle BAE={60}^{\circ }$, then $\angle BAC$ will be

1. ${60}^{\circ }$

2. ${15}^{\circ }$

3. ${30}^{\circ }$

4. ${10}^{\circ }$

Q.

We can use the concept of an equilateral triangle to construct a 60${}^{\circ }$ angle.

1. True

2. False

Q.

We can use the concept of an equilateral triangle to construct a 60${}^{\circ }$ angle.

1. True

2. False

Q. Find the length of arc if the angle subtended at its center is ${75}^{\circ }$ and circumference is $120cm$

Q.

In the given figure if $\angle$ BAC = ${60}^{\circ }$, AB = AC = 6cm then find the length of BC.

1. 6

2. 12

3. 10

4. 3

Q.

In the given figure if $\angle$BAC = ${60}^{\circ }$, AB = AC, then

1. 2BC = AC

2. AB = BC

3. BC = AC

4. AB > AC

Q. Construct a right angled $△ABC$ with $\angle B={90}^{\circ },BC=5cm$ and $AC=10cm$ and find the measure of $\angle C$ in degrees

Q.

With a ruler and compass which of the following angles cannot be constructed?

1. ${90}^{\circ }$
2. ${105}^{\circ }$

3. ${80}^{\circ }$

4. ${60}^{\circ }$

Q.

In the process of construction of ${45}^{\circ }$, which angle would be constructed first?

1. ${90}^{\circ }$
2. ${60}^{\circ }$
3. ${30}^{\circ }$
4. ${120}^{\circ }$

Q. Burst the bubbles with standard angles.

1. $0^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$
5. ${90}^{\circ }$
6. ${50}^{\circ }$
7. ${15}^{\circ }$
8. ${135}^{\circ }$