Question

What is the measure of 1

Answer 1

the measure of ∠1 is 92 degrees

Answer 2

Answer:
`92^(\circ)`

Explanation:

The measure of angles in the given quadrilateral are:
`62^(\circ), 92^(\circ), 114^(\circ)\text{ and }\angle{1}`.

We know that the sum of all angles of a quadrilateral is
`360^(\circ)`.

i.e.
`62^(\circ)+ 92^(\circ)+114^(\circ)+\angle{1}=360^(\circ)`.

Simplify left side , we get

`268^(\circ)+\angle{1}=360^(\circ)`

Subtract
`268^(\circ)` from bnoth the sides , we get

`\angle{1}=360^(\circ)-268^(\circ)\\\\\Rightarrow \angle{1}=92^(\circ)`

Hence, the measure of
`\angle{1}=92^(\circ)`