Answer: [tex]92^{\circ}[/tex]
Step-by-step explanation:
The measure of angles in the given quadrilateral are:[tex]62^{\circ}, 92^{\circ}, 114^{\circ}\text{ and }\angle{1}[/tex].
We know that the sum of all angles of a quadrilateral is [tex]360^{\circ}[/tex].
i.e. [tex]62^{\circ}+ 92^{\circ}+114^{\circ}+\angle{1}=360^{\circ}[/tex].
Simplify left side , we get
[tex]268^{\circ}+\angle{1}=360^{\circ}[/tex]
Subtract [tex]268^{\circ}[/tex] from bnoth the sides , we get
[tex]\angle{1}=360^{\circ}-268^{\circ}\\\\\Rightarrow \angle{1}=92^{\circ}[/tex]
Hence, the measure of [tex]\angle{1}=92^{\circ}[/tex]
