+0  
 
0
14
1
avatar+4 

Point P is on the side of line AC of triangle ABC such that angle ACB =angle ABC, and angle ABC - angle ACB = 42 degrees. Find angle PBC in degrees.

 Mar 24, 2024
edited by Kyle111  Mar 24, 2024
 #1
avatar+743 
0

Here is a full solution.

 

Analyze the given information:

 

Point P is on side AC of triangle ABC.

 

Angles ACB and ABC are congruent (angle ACB = angle ABC).

 

The difference between angle ABC and angle ACB is 42 degrees (angle ABC - angle ACB = 42°).

 

Identify key properties of triangles:

 

The sum of angles in a triangle is always 180 degrees.

 

Solve for missing angle in triangle ABC:

 

Let x represent the unknown measure of angle ABC (and angle ACB by congruence).

 

From the triangle property: x + x + (x - 42) = 180°

 

Combine like terms: 2x - 42 = 180

 

Add 42 to both sides: 2x = 222

 

Divide both sides by 2 to find x: x = 111°

 

Find angle PBC:

 

Since angles ABC and ACB are congruent, each measures 111 degrees (as found previously).

 

Angle PBC is supplementary to angle ABC (they share a straight line).

 

Therefore, angle PBC = 180° - angle ABC = 180° - 111° = 69°.

 

Answer: Angle PBC = 69 degrees.

 Mar 26, 2024

1 Online Users