Intersecting Acute Angles

The intersecting acute angles measure the 0° and 90°. A sketch of angles is the main topic in geometry. Two lines join at a single point to form an angle.

If P and R are two straight lines they intersect at a point Q and make an angle Q. The angle Q is also represented as PQR. Here center point represents the vertex of the angle.

Example problems for intersecting acute angles:

Problem 1:-

Solving the intersecting acute angle from the where slopes  m1= 4 and m2=14

Solution:

In above diagram show the acute angles intersecting the two lines

tan phi = (m2- m1)/ (1+m1m2)

= (14-4)/(1+(14x4))

=10/ 57

= 0.175

Hence we find the phi value.

phi = arc tan(0.175)

from the tangent table,we get
phi =1o  (rounded value)



from the given example we can find the obtuse angle.

To subtract the acute angle between the the two values L,L2 from the 1800 straight angle.

That is,

phi = 180- phi

phi = 180 -1o

phi = 179o

Hence we find the obtuse angle.

Problem 2:-

Solving the intersecting acute angle from the where slopes  m1= 20 and m2=28

Solution:

In above diagram show the acute angles intersecting the two lines

tan phi = (m2- m1)/(1+m1m2)

= (28-20)/(1+(28x20)

= 8/ 561

= 0.0142

Hence we find the phi value.

phi   = arc tan(0.0142)

from the tangent table,we get
phi   = 1o  (rounded value)

from the given example we can find the obtuse angle.

the obtuse angle is calculated by subtracting the acute angle between the value of L and L2 from the straight angle 180 0

ie phi = 180- phi

phi = 180 -1o

phi = 179o

Hence we find the obtuse angle.

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Practice problems for intersecting acute angles:

1. Solving the intersecting acute angle from the where slopes  m1= 2 and m2=4

Answer:- 168o

2. Solving the intersecting acute angle from the where slopes  m1= 4 and m2= 8

Answer:- 173o

3. Solving the intersecting acute angle from the where slopes  m1= 8 and m2=12

Answer:- 178 o

4. Solving the intersecting acute angle from the where slopes  m1= 12 and m2=14

Answer:- 174 o