Find X: Solving Angles Between Parallel Lines with 110° and 105°

Question

110110110105105105XXX

What is the value of X given the angles between parallel lines shown above?

Video Solution

Solution Steps

00:00 Find X
00:03 The lines are parallel according to the given
00:08 We'll draw another line parallel to the lines
00:12 The sum of angles on a line equals 180
00:16 Subtract the known angle to find the desired angle
00:27 Alternate interior angles are equal between parallel lines
00:34 These are also alternate interior angles
00:37 The sum of angles equals the angle itself
00:42 Calculate to find X
00:50 And this is the solution to the question

Step-by-Step Solution

Due to the fact that the lines are parallel, we will begin by drawing a further imaginary parallel line that crosses the 110 angle.

The angle adjacent to the angle 105 is equal to 75 (a straight angle is equal to 180 degrees) This angle is alternate with the angle that was divided using the imaginary line, therefore it is also equal to 75.

In the picture we are shown that the whole angle is equal to 110. Considering that we found only a part of it, we will indicate the second part of the angle as X since it alternates and is equal to the existing X angle.

Therefore we can say that:

75+x=100 75+x=100

x=110−75=35 x=110-75=35

Answer

35°

More Questions

Related Subjects

Sum and Difference of Angles Angles In Parallel Lines Collateral angles Adjacent angles Vertically Opposite Angles Alternate angles Corresponding angles The Sum of the Interior Angles of a Triangle Sides, Vertices, and Angles Types of Angles Exterior angles of a triangle Sum of Angles in a Polygon

Question Types

Sum and Difference of Angles: Using angles in a triangle Angles in Parallel Lines: Using angles in a triangle