The measures of the arc JK and angle KIJ of the given inscribed triangle are; Arc JK = 104° and ∠KIJ = 52°
What is the measure of the angles?
We have been given the arc KI = 116°, so we can find the angle KJI by intercept property.
Angle KJI = arc KI/ 2
Thus;
Angle KJI = 116°/2
Angle KJI = 58°
Now by angle sum property of a triangle, we get:
∠ K + ∠ I + ∠ J = 180°
70° + ∠I + 58° = 180°
∠I = 52°
By using intercept formula, we get arc KJ;
∠JIK = arc JK/ 2
2(∠ JIK) = arc JK
2(52°) = arc JK
arc JK = 104°
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