Exercise 20B
Question 1
1. In each of the following, the measures of two angles are given, find the measure of the third angle of a triangle.
(i) $40^{\circ}, 70^{\circ}$
(i) $20^{\circ}, 80^{\circ}$
(iii) $40^{\circ}, 80^{\circ}$
(iv) $43^{\circ}, 65^{\circ}$
(v) $45^{\circ}, 106^{\circ}$
2. In each of the following, the measures of three angles are given. State in which case the angles can possibly be those of a triangle.
(i) $25^{\circ}, 65^{\circ}, 90^{\circ}$
(ii) $40^{\circ}, 71^{\circ}, 83^{\circ}$
(iii) $60^{\circ}, 60^{\circ}, 61^{\circ}$
(iv) $50^{\circ}, 60^{\circ}, 70^{\circ}$
(v) $28^{\circ}, 42^{\circ}, 110^{\circ}$
(vi) $57^{\circ}, 48^{\circ}, 83^{\circ}$
3. One of the acute angles of a right triangle is $62^{\circ}$. Find the other acute angle.
4. If two acute angles of a right triangle are equal. Find the two angles.
5. Each of the two angles of a triangle is twice the third angle. Find the angles of the triangle.
6. In the given figure, $\triangle P Q R$ is right angled at $P$, and $P S \perp Q R$. If $\angle Q=45^{\circ}$. Find
(ii) $\angle Q P S$,
(ii) $\angle \mathrm{PPS}$,
(iii) $\angle P R Q$
<img>
7.Find the lettered angles in the following figure.
8. Is it possible to have a triangle in which
(i) two of the angles are acute?
(ii) two of the angles are right angles?
(iii) two of the angles are obtuse?
(iv) each angle is less than $60^{\circ}$ ?
(v) each angle is greater than $45^{\circ}$ ?
(vi) each angle is greater than $60^{\circ}$ ?
(vii) each angle is equal to $60^{\circ}$ ?
9. In each of the figure given below, find
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(i) $\angle P X Y$.
(ii) $\angle AXB$.
10.In the given figure, find
<img>
(i) $\angle S Q R$
(ii) $\angle Q S R$
(iii) $\angle S Q P$
(iv) $\angle P$
11. In the given figure, find
<img>
(i) $\angle D A C$
(ii) $\angle A C D$
(iii) $\angle \mathrm{CAB}$
(iv) $\angle B$
12.In the given figure, find
<img>
(i) $\angle Q$
(ii) $\angle N M R$
(iv) $\angle P N M$
(v) $\angle M N R$
(iii) $\angle P M N$
(vi) $\angle M R N$
13. In the given figure, find
<img>
(i) $\angle A E B$
(iv) $\angle C F B$
(ii) $\angle B E F$
(iii) $\angle \mathrm{DFE}$
(v) $\angle C B F$
(vi) $\angle F B E$
Multiple Choice Questions (MCQs)
Tick (✔) the correct option.
14. One of the equal angles of an isosceles triangle is $36^{\circ}$. The third angle is
(a) $72^{\circ}$
(b) $36^{\circ}$
(c) $108^{\circ}$
(d) $54^{\circ}$
15. In the given adjacent figure, the value of $x$ will be
<img>
(a) $43^{\circ}$
(b) $97^{\circ}$
(c) $96^{\circ}$
(d) $62^{\circ}$
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