Activity to proove exterior angle property of a triangle
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Properties. An exterior angle of a triangle is equal to the sum of the opposite interior angles. For more on this see Triangle external angle theorem. If the equivalent angle is taken at each vertex, the exterior angles always add to 360° In fact, this is true for any convex polygon, not just triangles.
Interior Adjacent Angle : According to exterior angle ACX the interior adjacent angle in triangle ABC is ∠ACB. Relation between exterior and interior angles of triangle. Theorem : The measure of exterior angle is equal to the sum of two interior opposite angles.
Interior Adjacent Angle : According to exterior angle ACX the interior adjacent angle in triangle ABC is ∠ACB. Relation between exterior and interior angles of triangle. Theorem : The measure of exterior angle is equal to the sum of two interior opposite angles.
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As shown in the diagram:
Exterior Angle is ∠ ACD and its two interior opposite angles are ∠ BAC and ∠ ABC
Measure of ∠ ACD = 130°
Measure of one interior ∠ BAC = 60°
Measure of other interior ∠ ABC = 70°
Now, we can observe that:
130° = 60° + 70°
Or we can say:
∠ ACD = ∠ BAC and ∠ ABC
Hence, its demonstrated that measure of exterior angle of a triangle is equals to the sum of measures of its interior opposite angles
Exterior Angle is ∠ ACD and its two interior opposite angles are ∠ BAC and ∠ ABC
Measure of ∠ ACD = 130°
Measure of one interior ∠ BAC = 60°
Measure of other interior ∠ ABC = 70°
Now, we can observe that:
130° = 60° + 70°
Or we can say:
∠ ACD = ∠ BAC and ∠ ABC
Hence, its demonstrated that measure of exterior angle of a triangle is equals to the sum of measures of its interior opposite angles
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