Question:Ray BD bisects <ABC. The m<ABD=5× and m<DBC=3×+10. Find × and m<ABC
× is the multiplication operator
x is a variable name
Since BD bisects ABC, the angles ABD and DBC are equal. So,
5x = 3x+10
Now you can easily find x and ABC.
To find the values of × and m<ABC, we can set up an equation using the properties of angles formed by a bisector.
Given that Ray BD bisects angle <ABC, we know that m<ABD = m<DBC because they are vertical angles (they share the same vertex and are formed by intersecting lines). Therefore, we can set up an equation:
m<ABD = 5×
m<DBC = 3× + 10
Since BD bisects angle <ABC, the sum of m<ABD and m<DBC should be equal to m<ABC:
m<ABD + m<DBC = m<ABC
By substituting the given values, we get:
5× + 3× + 10 = m<ABC
Simplifying the equation gives:
8× + 10 = m<ABC
To find the value of ×, we need additional information or another equation relating to angle measures. Without additional information, × cannot be determined. However, we can determine the relationship between angle measures in terms of ×.
The equation 8× + 10 = m<ABC gives a relationship between × and m<ABC. For any value of ×, we can calculate m<ABC using this equation.