Question

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. For \(\angle4\) (an exterior angle of the triangle), \(m\angle4=m\angle1 + m\angle2\).

Step2: Use the linear - pair relationship

Since \(\angle3\) and \(\angle4\) form a linear pair (they are adjacent and supplementary), by the definition of supplementary angles (\(m\angle A+m\angle B = 180^{\circ}\) if \(A\) and \(B\) are supplementary), we have \(m\angle4=180 - m\angle3\).

Answer:

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