Question

Choose appropriate tools such as geometry software or a compass, straightedge, and protractor to inscribe quadrilateral GHU in a circle as shown in the figure. Then measure the angle at each vertex. V suppose mZHU is 67º and that memas. Can you find the measures of all the angles? Complete the explanation. Also, ZH HU and HG (select)y supplementary, so mZHGJ (select)- 67° = (select) and my are select) and have equal measures, so each angle must measure be found. (180°)- select the measures of all angles (select)

Answer 1

The sum of opposite angle of quadilateral is 180 degree. So,

$\angle IHJ+\angle IJG=180$

And

$\angle HGJ+\angle HIJ=180$

The sum of angle HIJ and angle HGJ is 180 degree. So there angle are supplementary angle.

Determine the measure of angle HGJ.

$\begin{gathered} \angle HGJ+67=180 \\ \angle HGJ=180-67 \\ =113 \end{gathered}$

The sum of angle H and angle J is also 180 so angle H and angle are supplemntary angles.

Determine the measure of angle H or angle J (Both are equal).

$\begin{gathered} \angle H+\angle J=180 \\ \angle H+\angle H=180 \\ \angle H=\frac{1}{2}\cdot180 \\ =90 \end{gathered}$

The measure of angle H and angle J is 90 degree.

So all four angles measure can be found.

Answer:

Blank 1: are

Blank 2: 180

Blank 3: 113

Blank 4: Supplementary

Blank5: 1/2(180) = 90

Blank 6: Yes

Blank 7: Can