The angles of the isosceles triangle are
vertex angle = 74
base angles = 53 degrees
How to find the angle measure
The angle measure is sought using the isosceles triangle theorem
From the theorem, we have the equation
(4x + 29) = (5x + 23)
5x - 4x = 29 - 23
x = 6
Solving for the angle
= 4 (6) + 29
= 24 + 29
= 53 degrees
The base angle are 53 degrees each. We solve for the vertex angle
vertex angle = 180 - 2(53)
vertex angle = 74