Question

a student begins to build a model of a downtown bridge in the city where he lives. he measures some of the angles formed by the sides of the model. the student says both x and y are 65. why is he incorrect? use the drop - down menus to explain your answer. click the arrows to choose an answer from each menu. the student is incorrect because x and y choose... . the angles with measures x° and 40° are choose... angles, so x = choose... . using the value of x to find y, y = choose... .

Explanation:

Step1: Identify angle - relationship for \(x\)

The \(40^{\circ}\) angle and \(x^{\circ}\) angle form a right - angle (90°).
Since they are complementary (\(x + 40=90\)), then \(x=90 - 40\).

Step2: Calculate the value of \(x\)

\(x = 50\)

Step3: Use the value of \(x\) to find \(y\)

The sum of angles in a triangle is \(180^{\circ}\). In the triangle with angles \(x = 50^{\circ}\), \(50^{\circ}\) and \(y\), we have \(50+50 + y=180\).
So \(y=180-(50 + 50)=85\)

Answer:

The student is incorrect because \(x\) and \(y\) are not equal. The angles with measures \(x^{\circ}\) and \(40^{\circ}\) are complementary angles, so \(x = 50\). Using the value of \(x\) to find \(y\), \(y = 85\).