in triangle ABC, Angle BAC= 80. and AB=AC and C is produced at P then exterior angle.is x. find the value of x Related: Exterior angle Property of Triangles - Lines and Angles, Class 9, Mathematics

Question

in triangle ABC, Angle BAC= 80. and AB=AC and C is produced at P then exterior angle.is x. find the value of x Related:  Exterior angle Property of Triangles - Lines and Angles, Class 9, Mathematics

Answer

Answer

Answer

130'=x

Answer

To find the value of the exterior angle in triangle ABC, where angle BAC is 80 degrees and AB = AC, we can make use of the Exterior Angle Property of Triangles.

Exterior Angle Property of Triangles:
According to this property, the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

Given:
Angle BAC = 80 degrees
AB = AC

Step 1: Find the measures of angles B and C:
Since AB = AC, triangle ABC is an isosceles triangle. In an isosceles triangle, the base angles are congruent. So, angle ABC = angle ACB.
Let's assume angle ABC = angle ACB = y.

Since the sum of angles in a triangle is 180 degrees, we can write:
80 + y + y = 180
2y + 80 = 180
2y = 180 - 80
2y = 100
y = 100/2
y = 50

So, angle ABC = angle ACB = 50 degrees.

Step 2: Find the measure of the exterior angle, x:
The exterior angle is formed by extending one side of the triangle. In this case, we extend side AC to point P.

Since angle BAC is an interior angle and angle x is an exterior angle, we have:
x = 180 - 80
x = 100 degrees

Conclusion:
The value of the exterior angle, x, in triangle ABC is 100 degrees.

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