Answer :

Answer:  266 degrees

Explanation

The tick marks tell us that the triangle is isosceles. The angles opposite those congruent sides are congruent in measure. These are the base angles.

The base angles are 43 degrees each. Let x be the missing interior angle of this triangle.

Recall that all three inside angles of a triangle always add to 180 degrees.

43+43+x = 180

86+x = 180

x = 180-86

x = 94

Then notice how angles w and x add to 360 degrees, since they sweep out a full circle or full rotation.

w+x = 360

w+94 = 360

w = 360-94

w = 266

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Answer:

[tex]266^\circ[/tex]

Step-by-step explanation:

I will label the triangle as shown below.

Here, we know, WX = WY. Hence, WXY is an isosceles triangle.

Now,

 [tex](\text{i})\ \angle X=\angle Y\ \ \ [\text{Base angles of isosceles triangle are equal.}]\\\text{or, }\angle X=\angle Y=43^\circ[/tex]

[tex]\text{(ii) }\angle W +\angle X+\angle Y=180^\circ\ \ \ [\text{Sum of angles of triangle is 180}^\circ.]\\\text{or, }\angle W+43^\circ+43^\circ=180^\circ\\\text{or, }\angle W=180^\circ-86^\circ\\\text{or, }\angle \text{W}=94^\circ[/tex]

Finally, we need to calculate the reflex angle W.

[tex]\text{(iii)\ }\text{ref. }\angle W=360^\circ-\angle W=360^\circ-94^\circ=266^\circ[/tex]

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