which of the following measure can be used to construct a unique triangle give reason for your answers angle A=45 angle B=80 angle C=65
Answers
Answer:
Page No 196:
Question 1:
Take three noncollinear points A, B and C on a page of your notebook. Join AB, BC and CA. What figure do you get?
Name: (i) the side opposite to ∠C
(ii) the angle opposite to the side BC
(iii) the vertex opposite to the side CA
(iv) the side opposite to the vertex B
Figure
ANSWER:
We get a triangle by joining the three non-collinear points A, B and C.
(i) The side opposite to ∠C is AB.
(ii) The angle opposite to the side BC is ∠A.
(iii) The vertex opposite to the side CA is B.
(iv) The side opposite to the vertex B is AC.
Page No 196:
Question 2:
The measures of two angles of a triangle are 72° and 58°. Find the measure of the third angle.
ANSWER:
The measures of two angles of a triangle are 72° and 58°.
Let the third angle be x.
Now, the sum of the measures of all the angles of a triangle is 180o.
∴∴ x + 72o + 58o = 180o
⇒ x + 130o = 180o
⇒ x = 180o −- 130o
⇒ x = 50o
The measure of the third angle of the triangle is 50o.
Page No 196:
Question 3:
The angles of a triangle are in the ratio 1 : 3 : 5. Find the measure of each of the angles.
ANSWER:
The angles of a triangle are in the ratio 1:3:5.
Let the measures of the angles of the triangle be (1x), (3x) and (5x)
Sum of the measures of the angles of the triangle = 180o
∴ 1x + 3x + 5x = 180o
⇒ 9x = 180o
⇒ x = 20o
1x = 20o
3x = 60o
5x = 100o
The measures of the angles are 20o, 60o and 100o.
Page No 196:
Question 4:
One of the acute angles of a right triangle is 50°. Find the other acute angle.
ANSWER:
In a right angle triangle, one of the angles is 90o.
It is given that one of the acute angled of the right angled triangle is 50o.
We know that the sum of the measures of all the angles of a triangle is 180o.
Now, let the third angle be x.
Therefore, we have:
90o + 50o + x = 180o
⇒ 140o + x = 180o
⇒ x = 180o −- 140o
⇒ x = 40o
The third acute angle is 40o.
Page No 196:
Question 5:
One of the angles of a triangle is 110° and the other two angles are equal. What is the measure of each of these equal angles?
ANSWER:

Given:
∠A = 110o and ∠B = ∠C
Now, the sum of the measures of all the angles of a traingle is 180o .
∠A + ∠B + ∠C = 180o
⇒ 110o + ∠B + ∠B = 180o
⇒ 110o + 2∠B = 180o
⇒ 2∠B = 180o −- 110o
⇒ 2∠B = 70o
⇒ ∠B = 70o / 2
⇒ ∠B = 35o
∴ ∠C = 35o
The measures of the three angles:
∠A = 110o, ∠B = 35o, ∠C = 35o
Page No 196:
Question 6:
If one angle of a triangle is equal to the sum of other two, show that the triangle is a right triangle.
ANSWER:
Given:
∠A = ∠B + ∠C
We know:
∠A + ∠B + ∠C = 180o
⇒ ∠B +∠C + ∠B + ∠C = 180o
⇒ 2∠B + 2∠C = 180o
⇒ 2(∠B +∠C) = 180o
⇒ ∠B + ∠C = 180/2
⇒ ∠B + ∠C = 90o
∴∴ ∠A = 90o
This shows that the triangle is a right angled triangle.
Page No 196:
Question 7:
In a ∆ABC, if 3∠A = 4 ∠B = 6 ∠C, calculate the angles.
ANSWER:
Let 3∠A = 4 ∠B = 6 ∠C = x
Then, we have:
∠A = x3, ∠B = x4, ∠C = x6But, ∠A + ∠B + ∠C = 180°∴ x3 + x4 + x6 = 180°or 4x + 3x + 2x12 = 180°or 9x = 180° × 12 = 2160°or x = 240° ∴ ∠A = 2403 = 80°, ∠B = 2404 = 60°, ∠C = 2406