Question

in rectangle erpl, find a + b in terms of c. after you pick your answer press go. a. a + b = 90 - c b. a + b = 180 - c c. a + b = 2c d. a + b = 90 + c e. a + b = c - 90

Explanation:

Step1: Use property of rectangle

In rectangle \(ERPL\), \(ER\parallel PL\). Let's draw a line parallel to \(ER\) and \(PL\) through the intersection point of the non - diagonal lines.
By the property of alternate interior angles, we can use the angle - addition property.
Let's assume a line \(l\) parallel to \(ER\) and \(PL\) passing through the vertex of angles \(a\) and \(b\).
We know that in a rectangle, each angle is \(90^{\circ}\).
Let's consider the right - angled triangle formed by the diagonal \(PR\) and the sides of the rectangle.
We use the fact that the sum of angles in a right - angled triangle.
Let's assume the right - angled triangle at \(P\).
We know that \(a + b+ c=90^{\circ}\) (by constructing a right - angled triangle and using angle addition with the help of parallel lines in the rectangle).

Step2: Solve for \(a + b\)

Rearrange the equation \(a + b + c=90^{\circ}\) to get \(a + b=90 - c\)

Answer:

A. \(a + b = 90 - c\)