If solar panels are mounted parallel to the roof, then the panel tilt angle is the same as the slope of the roof. There are handy devices to measure angles, but it can also be done with a level, possibly a square, and either a protractor or a tape measure. Lay two boards on the roof on top of each other and lift one end of the top board until it is horizontal (level bubble centered). The tilt angle ("a") can be measured directly using a protractor with the center point where the boards meet. Another way is to consider the right triangle formed by the lower board, the horizontal upper board, and a vertical line between them (using the level or a square to determine vertical). Measure the length of the horizontal (H) and vertical (V) sides of the right triangle, then divide them (V/H), then take the inverse tangent of the result.
The horizontal direction that solar panels face refers to an angle measured from True North (or "map North"), rather than Magnetic North as measured by a compass. These are different because the magnetic north pole is not right at the geographic north pole (the axis of the Earth's spin). The difference between the two is the "magnetic declination", and it must be added to a compass measurement to determine a True (or map) direction. Good maps will show the local magnetic declination, which varies by location because the Earth's magnetic field has irregularities from deposits of magnetic rock, and it changes with time because the source of the magnetic field in the Earth's core is dynamic. The magnetic declination for any location can be found with the NOAA declination calculator. Good compasses can be adjusted for the local magnetic declination, so that the bearing on the compass will be relative to True North and no correction is needed. To measure the panel orientation angle, stand facing the direction the panels will face with the compass leveled in front of you, and be sure you're not near a lot of metal (including a belt buckle) or near power lines or other electrical currents because these modify the Earth's magnetic field and change the direction of the compass needle. Read the compass bearing and add the declination if not already set in the compass (or subtract the declination if Magnetic North is West of True North). By the way, the Earth's magnetic field reverses polarity (North becomes South and vice versa) every half million years or so, and we're due for a magnetic pole reversal any millenium now.