Math Problem Statement

BEG is a triangle. ABC and DEF are parallel lines. Work out the size of angle x. Give a reason for each stage of your working.

Solution

To solve for angle xx, we need to analyze the geometric relationships given in the diagram and use the fact that lines ABCABC and DEFDEF are parallel.

Step-by-Step Solution:

  1. Identify Corresponding Angles: Since lines ABCABC and DEFDEF are parallel, and line BEBE acts as a transversal, we know that the angle at BB (35°) is equal to the angle at EE (110° - 25°), because they are corresponding angles.

  2. Calculate the Angle at Point EE: The angle at EE is given as 110° (an exterior angle to triangle DEFDEF) and there is another angle adjacent to it (25°). To find the interior angle at EE: E=11025=85\angle E = 110^\circ - 25^\circ = 85^\circ

  3. Use Alternate Interior Angles: Angle GG equals angle FF, and since line is parallel, and we know that: G=110.\angle G = 110^\circ.

To solve correctly and accurately.

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Math Problem Analysis

Mathematical Concepts

Parallel Lines
Transversal Lines
Corresponding Angles
Interior Angles

Formulas

Corresponding Angles are Equal
Sum of Angles in a Triangle = 180°

Theorems

Corresponding Angles Theorem
Angle Sum Property of Triangles

Suitable Grade Level

Grades 9-10