sat suite question viewer

Geometry and Trigonometry / Lines, angles, and triangles Difficulty: Easy

In the figure, line $m$ is parallel to line $n$ . What is the value of $w$ ?

Back question 4 of 79 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

Explanation

Choice D is correct. It's given that lines $m$ and $n$ are parallel. Since line $t$ intersects both lines $m$ and $n$ , it's a transversal. The angles in the figure marked as $170 degree$ and $w °$ are on the same side of the transversal, where one is an interior angle with line $m$ as a side, and the other is an exterior angle with line $n$ as a side. Thus, the marked angles are corresponding angles. When two parallel lines are intersected by a transversal, corresponding angles are congruent and, therefore, have equal measure. It follows that $w degree equals 170 degree$ . Therefore, the value of $w$ is $170$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.