What is the value of m?
Understand the Problem
The question is asking for the value of angle 'm' which is formed by two intersecting lines. One of the angles is given as 46.8°, and the user needs to determine the measurement of angle 'm' based on the properties of angles formed by intersecting lines.
Answer
The value of \( m \) is \( 133.2^\circ \).
Answer for screen readers
The value of angle ( m ) is ( 133.2^\circ ).
Steps to Solve
-
Identify the angles formed by intersecting lines
When two lines intersect, they form two pairs of vertical angles. Vertical angles are equal, and the adjacent angles are supplementary. -
Set up the equation
Given that one angle is $46.8^\circ$, the adjacent angle $m$ can be found using the property of supplementary angles: $$ m + 46.8^\circ = 180^\circ $$ -
Solve for angle 'm'
To find the value of $m$, rearrange the equation: $$ m = 180^\circ - 46.8^\circ $$ -
Calculate the result
Now perform the calculation: $$ m = 180 - 46.8 = 133.2^\circ $$
The value of angle ( m ) is ( 133.2^\circ ).
More Information
The problem uses the properties of vertical and supplementary angles to determine the measurement of angle ( m ). This principle is fundamental in geometry, especially when dealing with intersecting lines.
Tips
- Confusing vertical angles with adjacent angles: Remember that vertical angles are equal, while adjacent angles are supplementary.
- Incorrectly adding the angles: Be sure to subtract the known angle from 180° rather than adding.
