Can I please get an explanation and answer for this problem.

It would be 42.

To solve this, first look at the information we're given. We know that the shape the missing angle is part of is a triangle, so therefore, the sum of the interior angles will always be 180 degrees. There is a right angle inside of the triangle. One of the exterior angles is 132 degrees.

The first thing we can see from this is that the two interior angles which are not right angles must add up to 90 degrees. Since the sum of all the interior angles is 180 degrees, and there is already a 90 degree angle, the other two must add up to 90 degrees.
The next step would then be to find the other interior angle which is not the missing angle. We can do this because of the exterior angle.
A straight line always has a measure of 180 degrees. In this case, we can see that the line the exterior angle is resting on is straight, and the exterior angle + the other interior angle = the line. Therefore, 132 + the other interior angle must equal 180 degrees.
Subtract 132 from both sides, and you get the other interior angle has a measure of 48 degrees.
Now, to take that and figure out the missing angle.
We know that the angle with a measure of 48 degrees and the missing angle must add up to 90 degrees, as stated above.
48 + missing angle = 90
Subtract 48 from both sides, and you get the measurement of the missing angle is 42 degrees.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.