An exterior angle of a triangle measures 110°. If the interior opposite angles are equal, find the measure of all the angles of the triangle.
Answers
Answer:
Let the given interior opposite angles be (2x)
o
and (3x)
o
We know that an exterior angle of a triangle is equal to the sum of its interior opposite angles.
∴ 2x+3x=110
o
5x=110
x=110/5=22
∴ ∠A=2x=2=2×22=44
o
∠B=3x=3×22=66
o
But ∠A+∠B+∠C=180
o
44
o
+66
o
+∠C=180
o
110+∠C=180
o
∠C=180−110
∠C=70
o
∠A=44
o
, ∠B=66
o
, ∠C=70
o
please brainlest mark
Answer:
According to property of triangle, measure of exterior angle of a triangle is the sum of other two non adjecent angles of triangle.
so here the sum of 2 given angles must measure up to 110°.
Given that the two interior opposite angles are in the ratio 2:3.
so let X be the common multiple
So 2x+3x= 110
5x=110
X=110/5
=22
So 1st angle is 22×2=44 degree
and 2nd is 22×3=66 degree
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