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Find the unknown angles in the figures below.
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Solution
The sum of all 3 interior angles of a triangle is equal to 180°. Hence
92 + 27 + x = 180
Solve for x
x = 180 - (92 + 27) = 61°
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Solution
The sum of all 3 interior angles of the right triangle is equal to 180°. Hence
y + 34 + 90 = 180
Solve for y
y = 180 - (90 + 34) = 56°
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Solution
Angle y and angle of measure 56°
are supplementary. Hence
y + 56° = 180°
Solve for y
y = 180 - 56 = 124°
Angle x and angle of measure 144°
are supplementary. Hence
x + 144 = 180°
Solve for x
x = 180 - 144 = 36°
The sum of angles x, y and z of the triangle is equal to 180°
x + y + z = 180
Substitute x and y by their values found above.
36 + 124 + z = 180
Solve for z.
z = 20°
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Solution
Let z be the third angle of the triangle on the right. The sum of the interior angles in the triangle on the right side is equal to 180°. Hence
26 + 26 + z = 180
z = 180 - 26 - 26 = 128°
Angles z and y are supplementary. Hence
z + y = 180
Solve for y
y = 180 - z = 180 - 128 = 52°
The sum of the interior angles in the angle on the left is equal to 180. Hence
x + y + 64 = 180°
Solve for x
x = 180 - 64 - 52 = 64°
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Solution
Angle z and the angle of measure 133° are supplementary angles. Hence
z + 133 = 180
z = 180 - 133 = 47°
The angles of the lower triangle add up to 180°. Hence
33 + 133 + x = 180
x = 180 - 33 - 133 = 14°
The sum of the measures of the angles of the upper triangle is equal to 180°. Hence
y + z + 114 = 180
y = 180 - 114 - Z , z = 47 found before
y = 180 - 114 - 47 = 19°
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Solution
The sum of the angles of the triangle on the right side is equal to 180°. Hence
w + 131 + 32 = 180
w = 180 - 131 - 32 = 17°
Angle v and the angle with measure 132° are supplementary. Hence
132 + v = 180
v = 180 - 132 = 48°
The three angles of the triangle in the middle add up to 180. Hence
v + z + 122 = 180
z = 180 - 122 - v
z = 180 - 122 - 48 = 10° , v = 48 found above
Angle x and the angle with measure 122° are supplementary. Hence
x + 122 = 180
x = 180 - 122 = 58°
The three angles of the triangle on the left side add up to 180. Hence
x + 43 + y = 180
y = 180 - 43 - x
y = 180 - 43 - 58 = 79° , x = 58 found above.
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