Question

5 numeric 1 point consider the circle. what is the measure of angle fih? answer 6 numeric 1 point consider the circle with diameter ec and center d. what is the measure of angle dfc? answer

Explanation:

Step1: Calculate the sum of known angles

The sum of angles around a circle is \(360^{\circ}\).

Step2: Find the measure of \(\angle FIH\)

We know two angles \(160^{\circ}\) and \(140^{\circ}\). Let \(\angle FIH = x\).

$$160 + 140+x=360$$

$$300+x = 360$$

$$x=360 - 300$$

$$x = 60$$

Step1: Use the property of a circle

The sum of angles around a circle is \(360^{\circ}\). Also, \(\angle EFC\) is a central - angle. Given \(\angle EFD=50^{\circ}\), and \(EC\) is a diameter so \(\angle EFC = 180^{\circ}\) (semicircle).

Step2: Find the measure of \(\angle DFC\)

Let \(\angle DFC=y\). We know \(\angle EFD + \angle DFC=\angle EFC\)
Since \(\angle EFC = 180^{\circ}\) and \(\angle EFD = 50^{\circ}\)

$$y=180 - 50$$

$$y = 130$$

Answer:

60