Which is the area of the figure?
1 answer:
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Answer:
three angles measuring 109º, 25º, and 145º cannot create a triangle
three angles measuring 40º, 70º, and 65º cannot create a triangle
Step-by-step explanation:
<u><em>Verify each dimensions</em></u>
Part 1) three angles measuring 109º, 25º, and 145º
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
In this problem we have
therefore
three angles measuring 109º, 25º, and 145º cannot create a triangle
Part 2) three sides measuring 9 m, 15 m, and 9 m
we know that
The <u><em>Triangle Inequality Theorem</em></u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Applying the triangle inequality theorem
1) 9+15 > 9 ---> is ok
2) 9+9 > 15 ---> is ok
therefore
three sides measuring 9 m, 15 m, and 9 m can create a triangle
Part 3) three angles measuring 40º, 70º, and 65º
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
In this problem we have
therefore
three angles measuring 40º, 70º, and 65º cannot create a triangle
Part 4) three sides measuring 6 cm, 8 cm, and 10 cm
we know that
The <u><em>Triangle Inequality Theorem</em></u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Applying the triangle inequality theorem
1) 6+8 > 10 ---> is ok
2) 8+10 > 6 ---> is ok
3) 6+10 > 8 ---> is ok
therefore
three sides measuring 6 cm, 8 cm, and 10 cm can create a triangle