Question

each row in the table below shows one possible set of angle measurements for this drawing. use the drawing and the given angle measurement to find the missing angle measurements. angle kgj angle jgi angle igh angle hgl 40 140 40 95 35 97

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. $\angle KGJ$ and $\angle IGH$ are vertical angles, and $\angle JGI$ and $\angle HGL$ are supplementary (linear - pair, sum to 180°).

Step2: First row with $\angle IGH = 35^{\circ}$

Since $\angle KGJ$ and $\angle IGH$ are vertical angles, $\angle KGJ=35^{\circ}$. Since $\angle JGI$ and $\angle HGL$ are supplementary and $\angle HGL$ is unknown, and $\angle JGI + \angle HGL=180^{\circ}$, then $\angle JGI = 180^{\circ}-\angle HGL$. Also, $\angle JGI$ and $\angle HGL$ are linear - pair. If $\angle IGH = 35^{\circ}$, then $\angle KGJ = 35^{\circ}$, and $\angle JGI=180 - 35=145^{\circ}$, $\angle HGL = 35^{\circ}$.

Step3: Second row with $\angle HGL = 97^{\circ}$

Since $\angle JGI$ and $\angle HGL$ are supplementary, $\angle JGI=180 - 97 = 83^{\circ}$. Since $\angle KGJ$ and $\angle IGH$ are vertical angles, and we know $\angle JGI = 83^{\circ}$, and $\angle IGH$ and $\angle JGI$ are supplementary to the angle formed by the straight - line, if we assume the straight - line angle is 180°, and $\angle JGI = 83^{\circ}$, then $\angle IGH=180 - 83=97^{\circ}$, and $\angle KGJ = 97^{\circ}$.

Answer:

angle KGJ	angle JGI	angle IGH	angle HGL
97	83	97	97