1. Two angles of a triangle are 40°,60° each. Find the measure of the exterior angles In the figure the larger angle is 50°more than the smaller angle.
pls help meeee
Answers
Answer:
Using the theorem that if the side of a triangle is produced then the interior angle is equal to the sum of two interior opposite angles of the triangle.
Let ΔABC be a triangle where the side BC is produced.
By the theorem we have
∠A+∠B=100
o
…………..(1)
It is given that the interior opposite angles are equal i.e., ∠A=∠B.
∴ Equation (1) becomes
2∠A=100
o
⇒∠A=50
o
⇒∠B=50
o
Using angle sum property of a triangle,
Sum of all angles of a triangle =180
o
⇒∠A+∠B+∠C=180
o
⇒100+∠C=180
o
[from (1)]
⇒∠C=180
o
−100
o
⇒∠C=80
o
.
Hence ∠A=50
o
∠B=50
o
∠C=80
o
.
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.