9514 1404 393
Answer:
y = 90°
Step-by-step explanation:
The angle sum theorem tells you the sum of angles in a triangle is 180°. You also know that the sum of the angles of a linear pair is 180°.
Let z represent the measure of the unmarked interior angle at the the lower left of the triangle shown. Then we have ...
110° + z = 180° . . . . angles of a linear pair are supplementary
z +2x +70° = 180° . . . Angle Sum theorem
Then we can write ...
110° +z = z +2x +70°
110° = 2x +70° . . . . . the exterior angle is equal to the sum of the remote interior angles.
40° = 2x . . . . . . . . . subtract 70°
20° = x
Similarly, we have ...
110° = x + y . . . . . . . exterior angle = sum of remote interior angles
110° -20° = y = 90° . . . . subtract x=20°
_____
<em>Additional comment</em>
You may be able to get there a lot faster by recognizing z = 180° -110° = 70°, hence the triangle is isosceles. The angle bisector creating angles x is then also an altitude, hence y = 90°.
