Answer:
see explanation
Step-by-step explanation:
x + y = 90 → (1) ( complementary angles )
x + z = 180 → (2) ( supplementary angles ) and
z = 3x - 8 ( 8 less than 3 times x ), substituting in (2)
x + 3x - 8 = 180
4x - 8 = 180 ( add 8 to both sides )
4x = 188 ( divide both sides by 4 )
x = 47
Substitute x = 47 into (1)
47 + y = 90 ( subtract 47 from both sides )
y = 43
and z = 3x - 8 = 3(47) - 8 = 141 - 8 = 133
Thus
x = 47°, y = 43° and z = 133°
The measures of all three angles should be x = 47°, y = 43° and z = 133°
We know that
In the complementary angles:
x + y = 90 ........ (1)
And, in supplementary angles
x + z = 180 ...... (2)
Now
z = 3x - 8
So,
x + 3x - 8 = 180
4x - 8 = 180
4x = 188
x = 47
Substitute x = 47 into (1)
47 + y = 90
y = 43
and
z = 3x - 8
= 3(47) - 8
= 141 - 8
= 133
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