Q. 3 Out of a pair of complementary angles, one of the angle is one-third of the other, find the angles Q. 4 In the given figure, \( P Q \) is a mirror, \( A B \) is the incident ray and \( B C \) is the reflected ray. if \( \angle A B C= \) then \( \angle A B P= \) ?

Q. 3 To solve this problem, let's denote the smaller angle as \( x \) and the larger angle as \( 3x \). Since the angles are complementary, their sum is 90 degrees. Therefore, we can set up the following equation: \[ x + 3x = 90 \] Combining like terms, we get: \[ 4x = 90 \] Now, we can solve for \( x \) by dividing both sides of the equation by 4: \[ x = \frac{90}{4} \] \[ x = 22.5 \] So, the smaller angle is 22.5 degrees, and the larger angle is three times that: \[ 3x = 3 \times 22.5 \] \[ 3x = 67.5 \] Therefore, the two complementary angles are 22.5 degrees and 67.5 degrees. Q. 4 In the given figure, \( PQ \) is a mirror, \( AB \) is the incident ray, and \( BC \) is the reflected ray. According to the law of reflection, the angle of incidence is equal to the angle of reflection. Since \( \angle ABC \) is the angle of incidence, \( \angle ABP \) is the angle of reflection. Given that \( \angle ABC = \theta \), then \( \angle ABP = \theta \) as well, because they are equal due to the law of reflection. Without the specific value of \( \theta \), we cannot determine the exact measure of \( \angle ABP \). However, we can express \( \angle ABP \) in terms of \( \theta \): \[ \angle ABP = \theta \] If you provide the value of \( \theta \), we can calculate the exact measure of \( \angle ABP \).