In each of the following figures, one side of a triangle has been produced. Find all the angles of the triangle in each case. (Please tell the circled part)
Answers
Given :-
The measure of exterior angle =80°
The measure of ∠A and the exterior angle=∠A+80=180(Linear pair)
The measure of :-
Which means :-
= ∠A+∠B+∠C=180°(angle sum property)
Then :-
(i) Measure of ∠B :-
Thus, the measure of ∠B=32°
(ii) Measure of ∠C :-
Thus, the measure of ∠C=48°
As the measure of all these three angles is adding upto form 180°, we can conclude that we have found out the correct measure of each of the angles of this triangle.
Therefore, the measure of ∠A=100° , ∠B=32° and∠C=48°.
Given :-
Measure of exterior angle B=140°
= ∠B + ∠y =180°(linear pair)
Thus, the measure of ∠y=40°
Moving forward :-
= ∠z + ∠C=180°(linear pair)
Thus, the measure of ∠z=50°
Which means :-
= ∠y + ∠z + ∠x =180°(angle sum property)
Thus, the measure of ∠x=90°
As the measure of all these three angles is adding upto form 180°, we can conclude that we have found out the correct measure of each of the angles of this triangle.
Therefore, the measure of ∠y=40°, ∠z=32° and∠x=90°.
Given :-
Measure of exterior angle C=125°
= ∠y + 125°=180°(linear pair)
Thus, the measure of ∠y=55°
Which means :-
= ∠B + ∠x + ∠y = 180°(angle sum property)
Thus, the measure of ∠x=70°
As the measure of all these three angles is adding upto form 180°, we can conclude that we have found out the correct measure of each of the angles of this triangle.
Therefore, the measure of ∠x=70° and ∠y=55° .
Given :-
The measure of exterior angle D=130°
= ∠D+∠B=180°(linear pair)
Thus, the measure of ∠B=50°
Which means :-
=∠B + ∠A + ∠C = 180°(angle sum property)
Thus, the measure of ∠B and∠C=65°
As the measure of all these three angles is adding upto form 180°, we can conclude that we have found out the correct measure of each of the angles of this triangle.
Therefore, the measure of ∠A=65° , ∠B=50° and ∠C=65°.