The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?
A. 40°
B. 70°
C. 100°
D. 140°
Answer (2)
The problem states that the triangle is isosceles with a vertex angle of 4 0 ∘ .
Recalling that the sum of angles in a triangle is 18 0 ∘ , we define the base angles as x and set up the equation 40 + 2 x = 180 .
Solving for x , we subtract 40 from both sides to get 2 x = 140 , and then divide by 2 to find x = 70 .
Therefore, the measure of a base angle is 7 0 ∘ .
Explanation
Problem Analysis Let's analyze the problem. We have an isosceles triangle, which means it has two equal angles (the base angles). We know the vertex angle (the angle between the two equal sides) is 40 degrees. We need to find the measure of one of the base angles.
Set up the equation The sum of the angles in any triangle is always 180 degrees. Let's call the measure of each base angle x . So, we can write the equation: vertex angle + base angle + base angle = 180 degrees, which translates to: 40 + x + x = 180
Solve for x Now, let's solve for x :
40 + 2 x = 180 Subtract 40 from both sides: 2 x = 180 − 40 2 x = 140 Divide both sides by 2: x = 2 140 x = 70
Final Answer Therefore, the measure of each base angle is 70 degrees.
Examples
Isosceles triangles are commonly found in architecture and engineering. For example, the supports of a bridge might form an isosceles triangle. Knowing the vertex angle allows engineers to calculate the base angles, ensuring structural stability and even weight distribution. This principle is also used in roof construction, where the slope and angle of the roof are crucial for water runoff and overall building integrity.
The measure of each base angle in the isosceles triangle with a vertex angle of 40° is 70°. Therefore, the correct multiple-choice option is B. 70° is the measure of the base angle.
;
