Question

4 what is the measure of angle 1? * (10 points) 54 42 46 100

Explanation:

Step1: Use the exterior - angle property of a triangle

The exterior - angle property of a triangle states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In \(\triangle GJH\), \(\angle JHG = 80^{\circ}\) is an exterior angle. So, \(\angle1+46^{\circ}=80^{\circ}\).

Step2: Solve for \(\angle1\)

Subtract \(46^{\circ}\) from both sides of the equation \(\angle1 + 46^{\circ}=80^{\circ}\). We get \(\angle1=80^{\circ}-46^{\circ}\).

Answer:

\(34^{\circ}\) (It seems there is a mistake in the original options. Using the correct geometric principle: \(\angle1 = 80^{\circ}-46^{\circ}=34^{\circ}\). If we assume the problem is about another property (maybe mis - labeled figure), and if we consider the sum of angles in a triangle. But if we follow the standard exterior - angle property calculation as above, the result is \(34^{\circ}\). If we consider the wrong approach of just looking at the options and assume a wrong property (which is not correct geometrically), there is an error in the given options. But if we force to choose from the given options, there is no correct one. However, if we use the formula \(\angle1=80 - 38\) (wrongly using another triangle's angle, which is not a valid geometric step), it's still wrong. The correct geometric answer based on \(\triangle GJH\) with exterior angle \(\angle JHG\) is \(34^{\circ}\))