Parallel Lines
Given that all three of the horizontal lines are parallel, what is the measurement of the red angle in degrees?
Note : The diagram is not drawn to scale.
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3 solutions
Discussions for this problem are now closed
AHh I was so used to the right angle. I was thinking the answer was 120 x'D so i was like maybe 135 LOL
i don't know why it deceived me to think that the top triangle have a 90 - 60 - 60 angles :D :D
thank you so much.
Solution 1:
Tip: Know the Properties of Parallel Lines.
Tip: An exterior angle in a triangle equals the sum of the two nonadjacent interior angles.
Refer to the diagram below.
x and a are alternate interior angles. Therefore x = a . The two transversals and line p form a triangle, shown in the figure in green. We know that in a triangle, the measure of an exterior angle equals the sum of the measures of the two nonadjacent interior angles. Therefore, y = a + 9 0 = x + 9 0 , which is choice (B).
Solution 2:
Tip: Know the Properties of Parallel Lines.
Tip: The two acute angles in a right triangle are complementary.
Refer to the diagram below.
x and a are vertical angles. Therefore x = a .
a and b are the acute angles in a right triangle, shown in green, and therefore add to 9 0 ∘ . It follows that b = 9 0 − a .
y and b are same-side exterior angles. Same-side exterior angles are supplementary and therefore y + b = 1 8 0 . We solve this equation:
y + b y y \ y y y = = = = = = 1 8 0 1 8 0 − b 1 8 0 − ( 9 0 − a ) 1 8 0 − 9 0 + a 9 0 + a 9 0 + x same-side exterior angles are supplementary substitute b = 9 0 − a
Right, but the image is wrong. It suggests the idea that the triangle is isosceles. In that case, the angle you claim to be 60°, would be 45°.
The image is not wrong. It may look like an isosceles triangle but it's not.
The 6 0 ° clearly indicates that it's not an isosceles triangle.
Edit: Whoever downvoted my comment should indicate and explain where I could be wrong at, not just downvoting and running away. You can't learn math this way.
there is a vertically opposite angle = 60 and if we consider the small right triangle we get the third side which is 30, the angle below it is also 30 ( corresponding angles ) now we know that a straight line = 180 degrees therefore 30+ red angle = 180 degrees, red angle = 150 degrees
Relevant wiki: SAT Lines and Angles