Question

1. if ( mangle2 = 112 ), what is ( mangle7 )?

( mangle7=)

1. select all the true statements given

the figure.
a. ( mangle4 = mangle2 )
b. ( mangle4 = mangle1 + mangle2 )
c. ( mangle4 = 180 - mangle3 )
d. ( mangle4 = mangle1 + mangle2 + mangle3 )
e. ( mangle4 = mangle3 + mangle1 )

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(m\angle4=m\angle1 + m\angle2\).

Step2: Use the linear pair relationship

Since \(\angle3\) and \(\angle4\) form a linear pair, \(m\angle3+m\angle4 = 180^{\circ}\), then \(m\angle4=180 - m\angle3\).

Answer:

B. \(m\angle4=m\angle1 + m\angle2\), C. \(m\angle4 = 180 - m\angle3\)