What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 42° and its congruent sides each measure 9 cm? Please express your answer as a number only.
In an isosceles triangle, the base angles are congruent. Let's denote the measure of the vertex angle as 'x'.
Since one of the base angles measures 42°, the other base angle is also 42°.
The sum of the interior angles of a triangle is always 180°.
Therefore, we can set up the equation: 42° + 42° + x = 180°.
Simplifying the equation: 84° + x = 180°.
Solving for 'x' by subtracting 84° from both sides: x = 180° - 84°.
Calculating: x = 96°.
So, the measure of the vertex angle is 96°.
To find the measure of the vertex angle of an isosceles triangle, we first need to find the measure of the base angle. Since it is given that one of the base angles measures 42°, we can determine that the other base angle is also 42° since isosceles triangles have two congruent base angles.
Next, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of the vertex angle. In this case, we have two base angles at 42° each, so the sum of these two angles is 42° + 42° = 84°.
To find the vertex angle, we subtract the sum of the base angles from 180°: 180° - 84° = 96°.
Therefore, the measure of the vertex angle of the isosceles triangle is 96°.
Triangle XYZ is isosceles. The measure of the vertex angle, Y, is twice the measure of a base angle.
What is true about triangle XYZ? Check all that apply.
If one base angle is 42, so is the other. And, the three angles total 180.
The length of the sides does not matter.