Question

1. find the measure of y. 120° 85° 53° 122° 138° 102° 85°

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral.

The sum of the interior angles of a quadrilateral is \( (4 - 2)\times180^{\circ}=360^{\circ} \).

Step2: Sum the known angles.

The known angles are \( 120^{\circ} \), \( 85^{\circ} \), and \( 53^{\circ} \). Their sum is \( 120^{\circ}+85^{\circ}+53^{\circ}=258^{\circ} \).

Step3: Solve for \( y \).

Let the sum of all angles be \( 360^{\circ} \). So, \( y = 360^{\circ}-258^{\circ}=102^{\circ} \)? Wait, no, wait. Wait, the figure is a quadrilateral? Wait, no, wait, the figure has four sides? Wait, no, looking at the diagram, it's a quadrilateral? Wait, no, wait, the angles given are 120, 85, 53, and y. Wait, no, wait, maybe I made a mistake. Wait, the sum of interior angles of a quadrilateral is 360? Wait, no, a quadrilateral has four sides, so sum is (4 - 2)*180 = 360. Wait, but let's recalculate the sum of known angles: 120 + 85 + 53 = 258. Then y = 360 - 258? Wait, no, that gives 102, but wait, maybe the figure is a pentagon? No, the diagram shows a four - sided figure? Wait, no, maybe I miscounted the sides. Wait, the figure has four angles: 120, 85, 53, and y. Wait, no, that's four angles, so quadrilateral. Wait, but 120 + 85 + 53 + y = 360? Then y = 360 - (120 + 85 + 53)=360 - 258 = 102? But the options have 102 as an option. Wait, but let me check again. Wait, maybe I made a mistake in the number of sides. Wait, the figure: let's count the sides. The diagram shows a four - sided figure? Wait, no, maybe it's a quadrilateral. Wait, 120 + 85 + 53 + y = 360. So 120+85 = 205, 205+53 = 258, 360 - 258 = 102. So y = 102 degrees.

Answer:

102° (corresponding to the option with 102°)