How do you find the missing variables in this problem please help

x = 55, y = 70, z = 125

Step-by-step explanation:

125 and x are adjacent angles and are supplementary, then

x = 180 - 125 = 55

The triangle is isosceles ( 2 congruent sides ) thus the base angles are congruent, both 55

The sum of the 3 angles in the triangle = 180° , thus

y = 180 - (55 + 55) = 180 - 110 = 70

55 and z are adjacent and supplementary, so

z = 180 - 55 = 125

Answers:

x = 55

y = 70

z = 125

Explanation:

The tick marks indicate those two lines are the same length. We have an isosceles triangle. One base angle is x. The other missing base angle is also x, which is adjacent to angle z. The base angles of any isosceles triangle are always congruent.

Since the 125 and x degree angle form a straight line, they must add to 180

x+125 = 180

x = 180-125

x = 55

We can use this to find y

x+x+y = 180 three angles of any triangle always add to 180

2x+y = 180

2(55)+y = 180 plug in x = 55

110+y = 180

y = 180-110

y = 70

And,

x+z = 180

55+z = 180 ... plug in x = 55

z = 180-55

z = 125

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