Answer :
Given:
The base JK of isosceles triangle HJK is produced to L and angle J=69 degrees.
To find:
The measure of angle HKL.
Solution:
According to the given information draw a figure as shown below.
In triangle HJK, JK is base and base angles of an isosceles triangle are congruent.
[tex]\angle HJK\cong \angle HKJ[/tex]
[tex]m\angle HJK=m\angle HKJ=69^\circ[/tex]
JKL is a straight line. So,
[tex]m\angle HKJ+m\angle HKL=180^\circ[/tex] (Linear pair)
[tex]69^\circ+m\angle HKL=180^\circ[/tex]
[tex]m\angle HKL=180^\circ-69^\circ[/tex]
[tex]m\angle HKL=111^\circ[/tex]
Therefore, the measure of angle HKL is 111 degrees.
