If the sum of the measures of ∠H and ∠J is 76∘ , what is the measure of ∠I ?

 HKJ = 100

Step-by-step explanation

In this problem we need to use the property of a inscribed angle:

The inscribed angle is a point in the circle that has endpoints also in the circle. The value of the inscribed angle is half the value of the arc formed by the endpoints.

So, If the arc FJ is 84°, we have that the angle in point G isi 84/2 = 42°

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

i think its a and d

step-by-step explanation: