Question

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) ​

Answer 1

$\color{plum}\tt{Solution \: \: (iii) : }$

Given :-

The measure of exterior angle =80°

The measure of ∠A and the exterior angle=∠A+80=180(Linear pair)

The measure of :-

$∠A = 180 - 80$

$\bold{∠A = 100}°$

Which means :-

= ∠A+∠B+∠C=180°(angle sum property)

$= 100 + 2x + 3x = 180$

$= 100 + 5x = 180$

$= 5x = 180 - 100$

$= 5x = 80$

$= x = \frac{80}{5}$

$= x = 16$

Then :-

(i) Measure of ∠B :-

$= 2 \times 16$

$=\bold{∠B = 32}°$

Thus, the measure of ∠B=32°

(ii) Measure of ∠C :-

$= 3 \times 16$

$= \bold{∠C = 48}°$

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°.

$\tt{\color{plum}Solution \: \: (iv): }$

Given :-

Measure of exterior angle B=140°

= ∠B + ∠y =180°(linear pair)

$= 140 + y = 180$

$= y = 180 - 140$

$= \bold{∠y = 40}°$

Thus, the measure of ∠y=40°

Moving forward :-

= ∠z + ∠C=180°(linear pair)

$= z + 130 = 180$

$= z = 180 - 130$

$=\bold{∠ z = 50}°$

Thus, the measure of ∠z=50°

Which means :-

= ∠y + ∠z + ∠x =180°(angle sum property)

$= 40 + 50 + x = 180$

$= 90 + x = 180$

$= x = 180 - 90$

$=\bold{ ∠x = 90}°$

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°.

$\tt{\color{plum}Solution \: \: (v): }$

Given :-

Measure of exterior angle C=125°

= ∠y + 125°=180°(linear pair)

$= y = 180 - 125$

$= \bold{∠y = 55}°$

Thus, the measure of ∠y=55°

Which means :-

= ∠B + ∠x + ∠y = 180°(angle sum property)

$= 55 + x + 55 = 180$

$= 110 + x= 180$

$=\bold{ ∠x = 70}°$

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° .

$\tt{\color{plum}Solution \: \: (vi): }$

Given :-

The measure of exterior angle D=130°

= ∠D+∠B=180°(linear pair)

$= 130 + B = 180$

$= B = 180 - 130$

$= \bold{∠B = 50}°$

Thus, the measure of ∠B=50°

Which means :-

=∠B + ∠A + ∠C = 180°(angle sum property)

$= 50 + x + x = 180$

$= 50 + 2x = 180$

$= 2x = 180 - 50$

$= 2x = 130$

$= x = \frac{130}{2}$

$= x = 65$

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°.