Question

What is the measure of 1

Answer 1

the measure of ∠1 is 92 degrees

Answer 2

Answer: $92^{\circ}$

Step-by-step 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 $\angle{1}=92^{\circ}$