Question

1. \\(\overrightarrow{hk}\\) bisects \\(\angle ghj\\). find \\(m\angle ghk\\) and \\(m\angle khj\\).

angle jhg measures 161.

a) \\(m\angle ghk=161,\\) \\(m\angle khj=80.5\\)

b) \\(m\angle ghk=80.5,\\) \\(m\angle khj=80.5\\)

c) \\(m\angle ghk=80.5,\\) \\(m\angle khj=161\\)

d) \\(m\angle ghk=161,\\) \\(m\angle khj=161\\)

8.

name this angle.

a) none of the above

b) right

c) obtuse

d) acute

Explanation:

Question 7

Step1: Recall Angle Bisector Definition

An angle bisector divides an angle into two equal parts. So, \( \overrightarrow{HK} \) bisecting \( \angle GHJ \) means \( m\angle GHK = m\angle KHJ \), and \( m\angle GHK + m\angle KHJ = m\angle GHJ \).

Step2: Calculate Each Angle

Given \( m\angle GHJ = 161^\circ \), let \( x = m\angle GHK = m\angle KHJ \). Then \( x + x = 161^\circ \), so \( 2x = 161^\circ \). Solving for \( x \), we get \( x=\frac{161^\circ}{2}=80.5^\circ \). Thus, \( m\angle GHK = 80.5^\circ \) and \( m\angle KHJ = 80.5^\circ \).

A right angle is an angle that measures \( 90^\circ \), and it is indicated by a square corner (the right angle symbol) in the diagram. An acute angle is less than \( 90^\circ \), an obtuse angle is greater than \( 90^\circ \) but less than \( 180^\circ \). Since the diagram has a square corner, this angle is a right angle.

Answer:

b) \( m\angle GHK = 80.5 \), \( m\angle KHJ = 80.5 \)

Question 8