One of the interior opposite angles of a triangle is 400
and the exterior angle is 1200
. Find the
measures of the other two angles of the triangle
please help me
Answers
Answer:
Here Is your answer
Step-by-step explanation:
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
.
Given : One of the interior opposite angles of a triangle is 40° and the exterior angle is 120° .
To Find : the measures of the other two angles of the triangle.
Solution:
Method 1 :
Exterior angle of a triangle form a linear pair with the angle of triangle
Hence 120° + x = 180°
=> x = 60°
Sum of the angles of a triangle = 180°
Hence 60° + 40° + y = 180°
=> y = 80°
Hence 60° and 80° are other two angles
Method :
Exterior angle of triangle = Sum of opposite two interior angles
120° = 40° + y
=> y = 80°
Sum of the angles of a triangle = 180°
Hence 80° + 40° + 8= 180°
=> x = 60°
Hence 60° and 80° are other two angles
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