Question

What is the measure of angle x

Angels are not necessarily drawn to scale

Answer 1

Answer:

$\boxed{\boxed{\sf \angle x=76^{\circ}}}$

Step-by-step explanation:

Given the diagram, we can see that ∠DIJ and ∠AIC are supplementary angles because they form a straight line.

∠DIJ and ∠JIC =180°

$\sf \angle DIJ+ 107=180$

Subtract 107 from both sides:

$\sf \angle DIJ+107-107=180-107$

$\sf \angle DIJ=73$

*Interior angles of a triangle always add up to 180*

$\sf \angle JDI+\angle DIJ+\angle DJI=180^{\circ}$

$\sf 31^{\circ}+73^{\circ}+\angle DJI=180^{\circ}$

$\sf \angle DIJ=76^{\circ}$

∠DJI and ∠x are vertical angles, therefore they are congruent.

∠x=76°

________________________________