Question

question 6 (multiple choice worth 2 points)
(interior and exterior angles mc)
in △jkl, ( mangle j = 67^{circ} ) and ( mangle l = 90^{circ} ). determine the measure of the exterior angle to ( angle k ).
( 23^{circ} )
( 113^{circ} )
( 157^{circ} )
( 78.5^{circ} )

question 7 (multiple choice worth 2 points)
(interior and exterior angles mc)
in triangle ( def ), ( mangle d=(3x + 27)^{circ} ), ( mangle e=(4x + 22)^{circ} ), and ( mangle f = 68^{circ} ). determine the degree n
( 54^{circ} )

Explanation:

Step1: Find the measure of ∠K

The sum of interior angles in a triangle is \(180^{\circ}\).
So, \(m\angle K=180^{\circ}-m\angle J - m\angle L\).
Substitute \(m\angle J = 67^{\circ}\) and \(m\angle L=90^{\circ}\):
\(m\angle K=180^{\circ}-67^{\circ}-90^{\circ}=23^{\circ}\).

Step2: Find the exterior angle to ∠K

The exterior angle of an angle is supplementary to the interior angle.
Let the exterior angle be \(x\). Then \(x + m\angle K=180^{\circ}\).
Since \(m\angle K = 23^{\circ}\), we have \(x=180^{\circ}-23^{\circ}=157^{\circ}\).

Answer:

\(157^{\circ}\)