Measures of two angles of a triangle are the same and the third angle is 80ᵒ. Find the measure of each angles.
Answers
Answer:
Given :
Measures of two angles of a triangle are the same and the third angle is 80ᵒ.
To Find :
Measure of each angle of the Triangle.
Solution :
\longmapsto\tt{Let\:the\:same\:angle\:be=x}⟼Letthesameanglebe=x
As we know that Sum of all angles of a Triangle is 180°. So ,
\longmapsto\tt{x+x+80^{\circ}=180^{\circ}}⟼x+x+80
∘
=180
∘
\longmapsto\tt{2x+80^{\circ}=180^{\circ}}⟼2x+80
∘
=180
∘
\longmapsto\tt{2x=180^{\circ}-80^{\circ}}⟼2x=180
∘
−80
∘
\longmapsto\tt{2x=100^{\circ}}⟼2x=100
∘
\longmapsto\tt{x=\cancel\dfrac{100}{2}}⟼x=
2
100
\longmapsto\tt\bf{x=50^{\circ}}⟼x=50
∘
So , The Measure of two same angles is 50° .
VERIFICATION :
\longmapsto\tt{x+x+80^{\circ}=180^{\circ}}⟼x+x+80
∘
=180
∘
\longmapsto\tt{50+50+80^{\circ}=180^{\circ}}⟼50+50+80
∘
=180
∘
\longmapsto\tt{100^{\circ}+80^{\circ}=180^{\circ}}⟼100
∘
+80
∘
=180
∘
\longmapsto\tt\bf{180^{\circ}=180^{\circ}}⟼180
∘
=180
∘
The sum of the interior angles of a triangle are equal to 180
o
.To find the third angle of a triangle when the other two angles are known subtract the number of degrees in the other two angles from 180
o
.
Therefore180
o
−30
o
−80
o
=70
o
.