What is the measure of a base angle of an isosceles triangle if its vertex angle measures 30?
30
150
15
75 <My choice
Which lengths could be the side lengths of a triangle?
18cm, 6cm, 13cm <My choice
13cm, 22cm, 7cm
6cm, 18cm, 12cm
22cm, 13cm, 8cm
yes 30 + 75 + 75 = 180
You choice is ok
the rest are not
7 and 13 will not reach 22
6 12 18 is a straight line again
13 + 8 = 21, will not reach
To find the measure of a base angle of an isosceles triangle, you can use the property that the base angles of an isosceles triangle are congruent. In this case, if the vertex angle measures 30 degrees, then each base angle will also measure the same amount.
Therefore, the measure of a base angle of the isosceles triangle with a vertex angle of 30 degrees is also 30 degrees.
For the question about the possible side lengths of a triangle, you can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's analyze the given options:
- 18cm, 6cm, 13cm: To determine if this could be the side lengths of a triangle, check if the sum of any two sides is greater than the third side. Here, 18 + 6 is greater than 13, 6 + 13 is greater than 18, and 13 + 18 is greater than 6. So, this set of side lengths could form a triangle.
- 13cm, 22cm, 7cm: Similarly, check the sum of any two sides. Here, 13 + 22 is greater than 7, but 7 + 13 is not greater than 22, violating the triangle inequality theorem. Therefore, this set of side lengths cannot form a triangle.
- 6cm, 18cm, 12cm: Again, check the sum of any two sides. Here, 6 + 18 is greater than 12, but 6 + 12 is not greater than 18, violating the triangle inequality theorem. Therefore, this set of side lengths cannot form a triangle.
- 22cm, 13cm, 8cm: Check the sum of any two sides. Here, 22 + 13 is greater than 8, 13 + 8 is greater than 22, and 22 + 8 is greater than 13. So, this set of side lengths could form a triangle.
Based on the triangle inequality theorem, the only set of side lengths that could form a triangle is 18cm, 6cm, 13cm.