the exterior angle 120degre and one interior angle 45degre of each triangle are given.find the other interior opposite angle and the third angle of each triangle.
The interior angle associated with the 120 degree exterior angle is its supplement: 60 degrees. With interior angles of 45 and 60 degrees, the third interior angle must be 180 - 105 = 75 degrees
See your first post.
Thanks drwls. I could not understand this post at all. :)
To find the other interior opposite angle and the third angle of each triangle, you can use the following steps:
Step 1: Understand the problem
In this problem, we are given an exterior angle of 120 degrees and one interior angle of 45 degrees in each triangle. We need to find the other interior opposite angle and the third angle of each triangle.
Step 2: Recall the properties of triangles
In any triangle, the sum of the three interior angles is always 180 degrees.
Step 3: Find the sum of the two known angles
Since one interior angle is given as 45 degrees, and the exterior angle is given as 120 degrees, we can find the sum of these two angles:
45 degrees + 120 degrees = 165 degrees
Step 4: Find the third angle
To find the third angle, subtract the sum of the two known angles from 180 degrees:
180 degrees - 165 degrees = 15 degrees
Step 5: Determine the other interior opposite angle
Since the sum of the three interior angles is always 180 degrees, the other interior opposite angle can be found by subtracting the given interior angle from 180 degrees:
180 degrees - 45 degrees = 135 degrees
Step 6: Verify the solution
To verify, add up the three interior angles of the triangle:
45 degrees + 135 degrees + 15 degrees = 180 degrees
Therefore, the other interior opposite angle is 135 degrees and the third angle is 15 degrees for each triangle.