Answer:
The value of k is 10.
Step-by-step explanation:
Triangles are flat fields bounded by 3 intersecting sides and 3 angles
This side can be the same length or different.
There are two angles that can form:
Supplementary Angles: if both angles are added = 180 °
Complementary Angles: if both angles are added = 90 °
From picture: ∠Y = Supplementary Angles:
115 ° + ∠Y = 180 °
∠Y = 180 ° - 115 °
∠Y = 65 °
As we know, the sum of all interior angles of a triangle = 180 °
So from the picture, the sum of ∠Y + ∠X + ∠Z = 180 °
65 ° + 6k + 10 ° + 4k + 5 ° = 180 ° (combine like terms)
65 ° + 10 ° + 5 ° + 6k + 4k = 180 °
80 ° + 10 k = 180 °
10 k = 180 ° -80 °
10 k = 100 °
k = 10
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