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.

Step2: Find $\angle KGJ$ when $\angle IGH = 35^{\circ}$

Since vertical angles are equal, $\angle KGJ=35^{\circ}$.

Step3: Use linear - pair property

$\angle KGJ$ and $\angle JGI$ form a linear - pair. A linear - pair of angles sums to $180^{\circ}$. So, $\angle JGI = 180^{\circ}-\angle KGJ$. When $\angle KGJ = 35^{\circ}$, $\angle JGI=180 - 35=145^{\circ}$.

Step4: Find $\angle HGL$

We know that the sum of angles around a point is $360^{\circ}$. Let's assume we are working with the angles related to the given ones. If we consider the angles in the context of the figure, and we know one of the non - given angles is $45^{\circ}$ (from the figure). Let's assume the sum of the four angles $\angle KGJ+\angle JGI+\angle IGH+\angle HGL + 45^{\circ}=360^{\circ}$. When $\angle KGJ = 35^{\circ}$, $\angle JGI = 145^{\circ}$, $\angle IGH = 35^{\circ}$, then $35 + 145+35+\angle HGL+45 = 360$. Simplifying the left - hand side gives $260+\angle HGL=360$. So, $\angle HGL=100^{\circ}$.

Step5: When $\angle HGL = 97^{\circ}$

Let $\angle IGH=x$. Using the sum of angles around a point $360^{\circ}$ and assuming the $45^{\circ}$ angle from the figure. Let $\angle KGJ = y$ and $\angle JGI = z$. We know $y + z+x + 97+45=360$. Also, $y = x$ (vertical angles). And $y+z = 180$ (linear - pair). Substituting $z = 180 - y$ into $y + z+x + 97+45=360$ gives $y+(180 - y)+x + 97+45=360$. Simplifying, $x+322 = 360$, so $x=\angle IGH = 38^{\circ}$, $\angle KGJ = 38^{\circ}$ and $\angle JGI=180 - 38 = 142^{\circ}$.

angle KGJ	angle JGI	angle IGH	angle HGL
38	142	38	97

Answer:

angle KGJ	angle JGI	angle IGH	angle HGL
38	142	38	97