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liraira [26]
3 years ago
6

Kevin is planting a triangular garden where 2 sides of the garden come together at an angle of 35°. If 1 unknown angle in the tr

iangle is 4 times as large as the second unknown angle in the triangle, what are the measures of the unknown angles in Kevin's triangular garden?
a. The second angle is 105, and the third angle is 29°

b. The second angle is 140°, and the third angle is 35º

c. The second angle is 120°, and the third angle is 30°.

d. The second angle is 116, and the third angle is 29°
Mathematics
1 answer:
Harrizon [31]3 years ago
3 0

Answer:

d. The second angle is 116, and the third angle is 29°

Step-by-step explanation:

second unknown angle be x

the other unknown angle = 4*x = 4x

x+ 4x + 35 = 180  {sum of all angles of triangle}

5x = 180-35 = 145

x = 145/5

x = 29

the other unknown angle = 4x = 4*29 = 116

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X = measure of angle 1
y = measure of angle 2
z = measure of angle 3
w = measure of angle 4

Focus on the bottom triangle. The three angles add to 180 degrees
(angle 2) + (angle 3) + 116 = 180
y+z+116 = 180
y+z= 180-116
y+z= 64

Since we have the bottom triangle as isosceles, this means that y = z, so
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y+y = 64
2y = 64
y = 64/2
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making z = 32 as well

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The figure is a rhombus because all four sides are the same length (as shown by the tickmarks)

-----------------------------------------------------------

Answer: 
This figure is a rhombus
All four angles (angle 1 through angle 4) are the same measure. They are each 32 degrees

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