Question

obtuse angle
name each angle in four ways.
5)
diagram of angle with points g, h, f
7)
diagram of angle with points k, l, j

1. ( mangle ghr = 22^circ ) and ( mangle rhi = 130^circ ). find ( mangle ghi ).

Explanation:

Problem 5: Naming the Angle (Assuming the angle at \( G \) with sides \( GH \) and \( GF \), and label \( \angle 5 \))

1. Using the vertex letter: The vertex is \( G \), so \( \angle G \).
2. Using the angle number: If the angle is labeled \( \angle 5 \), we can use \( \angle 5 \).
3. Using three points (with vertex in the middle) - first side, vertex, second side: The sides are \( GH \) and \( GF \), so \( \angle HGF \) (vertex \( G \) between \( H \) and \( F \)) and \( \angle FGH \) (vertex \( G \) between \( F \) and \( H \)).

1. Using the vertex letter: The vertex is \( K \), so \( \angle K \).
2. Using the angle number: If the angle is labeled \( \angle 5 \), we can use \( \angle 5 \).
3. Using three points (with vertex in the middle) - first side, vertex, second side: The sides are \( KJ \) and \( KL \), so \( \angle JK L \) (vertex \( K \) between \( J \) and \( L \)) and \( \angle LKJ \) (vertex \( K \) between \( L \) and \( J \)).

Step 1: Recall Angle Addition Postulate

The Angle Addition Postulate states that if a point \( R \) lies in the interior of \( \angle GHK \), then \( m\angle GHR + m\angle RHK = m\angle GHK \).

Step 2: Substitute the given values

We know that \( m\angle GHR = 22^\circ \) and \( m\angle RHK = 130^\circ \). So we substitute these values into the formula:
\( m\angle GHK = m\angle GHR + m\angle RHK \)
\( m\angle GHK = 22^\circ + 130^\circ \)

Step 3: Calculate the sum

\( 22^\circ + 130^\circ = 152^\circ \)

Answer:

\( \angle G \), \( \angle 5 \), \( \angle HGF \), \( \angle FGH \)

Problem 7: Naming the Angle (Angle at \( K \) with sides \( KJ \) and \( KL \), and label \( \angle 5 \))