Sure! Let's solve these problems step-by-step.
### Question 1:
Find the remaining angle in a right-angled triangle when one angle is 70°.
In any right-angled triangle, the sum of the angles is always 180°. One angle is always 90° (the right angle). Given that one of the other angles is 70°, we can find the remaining angle as follows:
1. The sum of the two non-right angles must be:
[tex]\[ 180° - 90° = 90° \][/tex]
2. One of the angles is given as 70°, so the remaining angle can be found by subtracting 70° from the 90° sum:
[tex]\[ 90° - 70° = 20° \][/tex]
So, the remaining angle is 20°.
### Question 2:
Find the remaining angle in radian measure when one angle is 72°.
1. In this problem, we again start with the fact that the sum of the non-right angles is:
[tex]\[ 90° \][/tex]
2. Given one of the angles is 72°, the remaining angle in degrees is:
[tex]\[ 90° - 72° = 18° \][/tex]
3. To convert the remaining angle from degrees to radians, we use the conversion factor:
[tex]\[ \text{Radians} = \text{Degrees} \times \left(\frac{\pi}{180}\right) \][/tex]
4. Substituting the remaining angle in degrees, we get:
[tex]\[ 18° \times \left(\frac{\pi}{180}\right) = \frac{18\pi}{180} = \frac{\pi}{10} = 0.3141592653589793 \][/tex] (approximately)
So, the remaining angle is approximately 0.314 rad.
### Summary of Solutions:
1. The remaining angle when one angle is 70° is 20°.
2. The remaining angle when one angle is 72° is approximately 0.314 radians (equivalent to 18°).
