Question

2 multiple choice 1 point
in the figure shown, ( ell_{1} parallel ell_{2} ) and ( ell_{3} perp ell_{4} ).
what is the value of ( x )?
33
123
57
147

Explanation:

Step1: Use the property of parallel lines

Since \( \ell_{1}\parallel\ell_{2}\), the corresponding angles formed by the transversal \( \ell_{4}\) are equal. Let's assume the angle adjacent to \(x\) (in the right - angled triangle formed by \( \ell_{3}\) and \( \ell_{4}\) with \( \ell_{2}\)) is equal to \(57^{\circ}\) (due to the parallel lines property).

Step2: Use the angle - sum property of a right - angled triangle

In a right - angled triangle (because \( \ell_{3}\perp\ell_{4}\), one angle is \(90^{\circ}\)), we know that the sum of angles in a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(90^{\circ}\), \(57^{\circ}\), and \(x\). Then \(x + 57^{\circ}+90^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(90^{\circ} + 57^{\circ})$$

$$x = 180^{\circ}-147^{\circ}$$

$$x=33^{\circ}$$

Answer:

33