Question

Find the measure of ZGHJ and LGIJ.68°H 31GK115angle GH) =degreesangle GIJ =degrees

Answer 1

Step 1: Find arc angle GJ

The sum of the arc angles of a circle is 360°.

Therefore,

$\begin{gathered}

step2: Find the angle GKJ, the angle subtended by the arc GJ

The angle GKJ is the angle subtended by the arc GJ at the center of the circle

Therefore,

[tex]<\text{GKJ }=\text{ m < GJ }=146^o$

Step 3: Find m < GHJ

From Circle theorem, we know that the angle at the center of a circle is twice the angle at the circumference

Therefore,

[tex]\begin{gathered} <\text{GKJ }=2\timesHence, m 73°Step 4: Find m < GIJFrom Circle theorem, the angles in the same segment are equalTherefore,[tex]<\text{GIJ }=Hence, m < GIJ = 73°