Answer:
Explanation:
You want to know angles x, y, and z in the given figure where parallel lines 'a' and 'b' are crossed by a transversal. The sum of these angles is 290°.
Consecutive interior angles
Angles y and z are called consecutive interior angles. As such, they are supplementary, so their sum is 180°.
x + y + z = 290°
x + 180° = 290°
x = 110°
Vertical angles
Angles x and y are vertical angles, so are congruent.
y = x = 110°
Then z is found from ...
y + z = 180°
110° + z = 180°
z = 70°
The measures of x, y, and z are 110°, 110°, and 70°, respectively.
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