Answer:
x = 111°
x° = 111°
(x-42)° = 69°
Step-by-step explanation:
Any polygon with *n* number of sides has an interior angle sum of (n-2) × 180°.
Therefore this right trapezoid must have an interior angle sum of 360° because
a trapezoid has 4 sides → n = 4 →
(n-2) × 180° = (4-2) × 180° = 2 × 180° = 360°
Because we are given a 90 degree angle with a set of parallel sides, the angle above that must also be a right angles well so these will total 180°.
The last two angles are given by the two expressions x°, and (x-42)°. Because we know the sum of these angles which are 360° we can create the following equation from these angles and solve!
180° + 2x - 42° = 360°
(Group the constants / numbers without a variable ; associative property of addition)
180° - 42° + 2x = 360°
(Find the total value of the constants)
138° + 2x = 360°
(subtract 138° from both sides to isolate 2x on the left side ; subtraction property of equality)
138° - 138° + 2x = 360° - 138°
(Work out the value of the constants again)
2x = 222°
(divide by 2 on both sides to cancel out the coefficient of 2 in 2x to get x by itself ; division property of equality)
2x / 2 = 222° / 2
(Simplify the two expressions)
x = 111°
_____________________
To find the measure of the x expressions, just substitute x = 111° into the expressions and simplify to find the measure!
So:
x = 111° → x° = 111°
x = 111° → (x-42)° → (111 - 42)° = (69)° →
(x-42)° = 69°
