Question

period: geometry exit ticket 2.05: swbat determine missing angles in diagrams using properties of parallel lines and triangles. directions: complete the following questions by showing all work and annotations. keep work organized and box any final answer. all work must be shown in order to receive full credit. **p.1 given ( ad parallel hf ). if ( mangle abg = 152^circ ), ( mangle bgc = 28^circ ), determine the ( mangle jgh ).

Explanation:

Step1: Find $\angle GBC$

Since $\angle ABG = 152^{\circ}$, and $\angle ABG+\angle GBC = 180^{\circ}$ (linear - pair of angles), then $\angle GBC=180^{\circ}-\angle ABG$.
Substitute $\angle ABG = 152^{\circ}$ into the formula: $\angle GBC=180 - 152=28^{\circ}$.

Step2: Find $\angle BCG$

In $\triangle BCG$, we know $\angle GBC = 28^{\circ}$.

Step3: Use the property of parallel lines

Since $AD\parallel HF$, then $\angle JGH=\angle BCG$ (corresponding angles).
First, find $\angle BCG$ using the exterior - angle property of a triangle.
The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
Let's consider the line $JE$ intersecting $AD$ and $HF$.
We know that $\angle ABG = 152^{\circ}$, so $\angle GBC=180 - 152 = 28^{\circ}$.
Since $AD\parallel HF$, $\angle JGH$ and $\angle BCG$ are corresponding angles.
We can also use the property of supplementary angles and parallel lines.
$\angle ABG$ and $\angle BGF$ are supplementary (because $AD\parallel HF$), so $\angle BGF=180 - 152=28^{\circ}$.
Then, $\angle JGH = 180-(28 + 28)=124^{\circ}$

Answer:

$124^{\circ}$