9514 1404 393
Answer:
Step-by-step explanation:
The hash marks indicate that the lower triangle is isosceles. That means its base angles are equal. The external angle marked 40° will be the sum of those two equal angles, so ...
x + x = 40°
x = 20°.
x is one of the two acute angles in the right triangle. The other is y, which is the complement of x.
y = 90° -x = 90° -20°
y = 70°
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Additional comments
The angle marked 40° is one of a "linear pair". The other angle in that pair is the obtuse angle in the lower triangle. Its measure is 180°-40° = 140°. The two base angles of that isosceles triangle are both x°, so you have ...
x° +x°+140° = 180°
2x° = 180° -140° = 40°
That is, the sum of the two angles will be equal to the external angle marked 40°. The relevant theorem says "an exterior angle is equal to the sum of the remote interior angles." Remembering this is a useful shortcut, so you don't have to find the third interior angle, which is 140° in this case.
