Create line segments at point coordinates in QGIS

One possible tool is Geometry by expression in the Processing Toolbox > Vector geometry.

A Geometry expression to create lines (length= 100 m) is as below:

make_line(project($geometry, 50, radians("angle")), project($geometry, 50, radians("angle"+180)))

• project($geometry, 50, radians("angle")) part creates a new point by moving your points to "angle" direction by 50 meters.
• project($geometry, 50, radians("angle"+180)) creates another point to the oposite direction.
• make_line() ties the above two points, so the total line length is 100 meters.
• project() function assumes that your "angle" is measured clockwise from north, so this expression may require edits depending on how your "angle" field is made.

NB. Do not forget saving created Modified geometry layer as a new dataset, otherwise it will be lost when you finish QGIS session.

I put an example of solving the same task with a pyqgis (3.2) standalone application. Below the python code

from qgis.core import QgsPointXY, QgsApplication, QgsVectorLayer, QgsFeature, QgsGeometry
from PyQt5.QtWidgets import QApplication
import sys
import math

def main():
    print('Start program')

    qgis_prefix_path = 'C:\\OSGeo4W64\\apps\\qgis'
    app = QApplication(sys.argv)
    QgsApplication.setPrefixPath(qgis_prefix_path, True)

    QgsApplication.initQgis()

    point_path = 'd:/Users/Bogomolov/Qgis/Test_prj/point.shp'
    line_path = 'd:/Users/Bogomolov/Qgis/Test_prj/lines.shp'
    point_layer = QgsVectorLayer(point_path, "pointlayer", "ogr")
    layer = QgsVectorLayer(line_path, "linelayer", "ogr")


    for feature in point_layer.getFeatures():
        geom: QgsGeometry = feature.geometry()
        pnt: QgsPointXY = geom.asPoint()
        length = feature['distance']
        bearing = feature['bearing']
        id = feature['id']
        print('id=', id)
        pnt0 = direct_geodetic_task(pnt, length / 2, bearing + 180)
        pnt1 = direct_geodetic_task(pnt, length / 2, bearing)
        points = []
        points.append(pnt0)
        points.append(pnt1)
        fields = layer.dataProvider().fields()
        feature = QgsFeature()
        feature.setGeometry(QgsGeometry.fromPolylineXY(points))
        feature.setFields(fields)
        feature.setAttribute('id', id)
        layer.dataProvider().addFeature(feature)

    # layer.commitChanges()

    QgsApplication.exitQgis()

def direct_geodetic_task(pnt, dist, bear):
    if bear > 360.0:
        bear = bear - 360
    if bear < 0:
        bear = 360 + bear

    deg = bear * math.pi / 180

    dx = dist * math.sin(deg)
    dy = dist * math.cos(deg)
    x = pnt.x() + dx
    y = pnt.y() + dy

    return QgsPointXY(x, y)

if __name__ == '__main__':
    main()

The result is the same