Question

I need help i don’t know how to do this

Answer 1

Answer:

EBGA

Step-by-step explanation:

The triangle is isosceles (XZ = YZ), so the base angles are congruent.  The total of all three angles in the triangle is 180 degrees, so subtracting out 52 leaves 128 degrees for the two base angles together.  Each base angles measures half of that, so $m\angle 1 = 64^\circ$, code E.

Look at vertex Y.  The big angle there also measures 64 degrees.

$m\angle 2 + 31^\circ =64^\circ\\m\angle 2= 64^\circ - 31^\circ = 33^\circ \text{ (code B)}$

Angle 3 is a vertical angle with the 88 degree angle, so its measure is also 88 degrees (code G).

Finally, angle 4 is an exterior angle in the small triangle that contains angles 2 and 3.  In that triangle, angles 2 and 3 are the remote interior angles.

$m\angle 4 = m\angle 2 + m\angle 3\\m\angle 4 = 33^\circ + 88^\circ = 121^\circ \text{ (code A)}$