Sum and Difference of Angles: Identify the greater value

The angle in diagram (a) is more acute, meaning it is smaller:

Conversely, the angle in diagram (b) is more obtuse, making it larger.

Note that in drawing B, the two lines form a right angle, which is an angle of 90 degrees:

While the angle in drawing A is greater than 90 degrees:

Therefore, the angle in drawing A is larger.

Answer B is correct because the more closed the angle is, the more acute it is (less than 90 degrees), meaning it's smaller.

The more open the angle is, the more obtuse it is (greater than 90 degrees), meaning it's larger.

In drawing A, we can see that the angle is more closed:

While in drawing B, the angle is more open:

In other words, in diagram (a) the angle is more acute, while in diagram (b) the angle is more obtuse.

Remember that the more obtuse an angle is, the larger it is.

Therefore, the larger of the two angles appears in diagram (b).

Note that in drawing A, the angle is a straight angle equal to 180 degrees:

While in drawing B, we are given a right angle, equal to 90 degrees:

Therefore, the angle in drawing A is larger.

In drawing A, we can see that the angle is an obtuse angle, meaning it is larger than 90 degrees:

While in drawing B, the angle is a right angle, meaning it equals 90 degrees:

Therefore, the larger angle appears in drawing A.

According to the diagram, angle B is a right angle equal to 90 degrees.

If we look at angle ACD, we can see that it is larger than 90 degrees.

We can also calculate angle ACD since it is supplementary to 180 degrees:

$180=ACB+ACD$

$180=40+ACD$

$180-40=ACD$

$140=ACD$

Therefore:

90 > 40

We can observe from the drawing that angle D is equal to 40 degrees,

We are also given that angle ACB is equal to 40 degrees. Therefore:

$D=ACB$

From the drawing, we can notice that we don't know the size of angle BAC

But if we pay attention, we'll see that angle BAE is equal to:

$BAC+CAE$

This means that angle BAE is necessarily larger than angle BAC since we are adding another angle to find its value.

Therefore:

BAE>BAC

From the drawing, it appears that angle BAE is equal to 90 degrees, therefore it can be argued that angle CAE is less than 90 degrees.

If we look at angle E, we can see that it is greater than 90 degrees, therefore:

E>CAE $$

According to the diagram, we are given that angle ACB is equal to 40 degrees.

Additionally, we are given that angle B is a right angle, meaning it is equal to 90 degrees.

Therefore:

B > ACB

Fist let's look at triangle ABC, remembering that the sum of angles in a triangle equals 180 degrees.

In triangle ABC, we are given two angles: 40 and 90.

Therefore, we can calculate BAC as follows:

$BAC=180-90-40$

$BAC=50$

Now let's look at angle E, noting that it is greater than 90 degrees.

Therefore:

E > BAC