Answers
Answer:
x = 24 degrees
Explanation:
The total of a triangle is 180 degrees. This problem can be broken into two triangles.
One triangle is 94 degrees, 41 degrees, and an unknown amount of degrees.
The other triangle is 111 degrees and two unknown amount of degrees.
Knowing 2 of the 3 degrees for the first triangle allows us to solve for this missing side:
180 - 94 - 41 = 45 degrees
This angle also applies to the second triangle, giving us a second known value. Now we know it has a 111 degree angle, a 45 degree angle, and an unknown angle. We can solve for the missing side the same was as before:
180 - 111 - 45 = 24 degrees
That means x = 24 degrees
Notice that the angle shown in red in the diagram belongs both to the bigger, outer triangle and the inner, smaller triangle.
Since the sum of the internal angles of every triangle must be equal to 180°, then:
A+94+41=180
x+A+111=180
Isolate A from the first equation:
A+94+41=180
⇒A+135=180
⇒A=180−135
⇒A=45
Substitute A=45 into the second equation and isolate x to find its value:
x+A+111=180
⇒x+45+111=180
⇒x+156=180
⇒x=180−156
⇒x=24
Therefore, the value of x is: x=24∘
