Question

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: Analyze the right triangle

In the right triangle with the \(40^\circ\) angle, the other non - right angle \(x\) and \(40^\circ\) are complementary (since the sum of angles in a triangle is \(180^\circ\) and one angle is \(90^\circ\)). So \(x + 40^\circ=90^\circ\).

Step2: Solve for \(x\)

From \(x + 40^\circ=90^\circ\), we can solve for \(x\) by subtracting \(40^\circ\) from both sides. So \(x = 90^\circ - 40^\circ=50^\circ\).

Step3: Analyze the straight line (angle sum on a straight line)

The angles \(x\), \(y\), and \(50^\circ\) lie on a straight line, so their sum is \(180^\circ\). We know \(x = 50^\circ\), so \(50^\circ+y + 50^\circ=180^\circ\).

Step4: Solve for \(y\)

First, simplify the left - hand side of the equation: \(100^\circ+y = 180^\circ\). Then subtract \(100^\circ\) from both sides: \(y=180^\circ - 100^\circ = 80^\circ\). So \(x\) and \(y\) are not equal. The angles with measures \(x^\circ\) and \(40^\circ\) are complementary angles, \(x = 50^\circ\), and \(y = 80^\circ\).

Answer:

The student is incorrect because \(x\) and \(y\) \(\boldsymbol{\text{are not equal}}\). The angles with measures \(x^{\circ}\) and \(40^{\circ}\) are \(\boldsymbol{\text{complementary}}\) angles, so \(x=\boldsymbol{50}\). Using the value of \(x\) to find \(y\), \(y = \boldsymbol{80}\).