The measures of two angles in this acute triangle are 38° and 72°. What is the measure of the third angle? A. 18° B. 33° C. 70°
1 answer:
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Answer:
The value of x is 0.5
The value of y is 0.8
The value of z is 0.9
Step-by-step explanation:
* Lets explain how to find the values of x , y and z
- <u><em>From the attached figure</em></u>
# and
intersect each other at a point
- When two lines intersect each other at a point they formed
congruent vertical opposite angles
∴ The angle of measure (50z + 13)° = the angle of measure (80z - 14)°
because thy are vertical opposite angles
∴ 50z + 13 = 80z - 14
- Add 14 to both sides
∴ 50z + 27 = 80z
- Subtract 50z from both sides
∴ 27 = 30z
- Divide both sides by 30
∴
* The value of z is 0.9
- <u><em>From the attached figure</em></u>
# The angles of measures (50z + 13)° and (45x + 19/2)° have sum
of 90°
∴ 50z + 13 + 45x + 19/2 = 90
∵ z = 0.9
∴ 50(0.9) + 13 + 45x + 19/2 = 90
∴ 45 + 13 + 45x + 9.5 = 90
- Add like term in the left hand side
∴ 67.5 + 45x = 90
- Subtract 67.5 from both sides
∴ 45x = 22.5
- Divide both sides by 45
∴ x = 0.5
* The value of x is 0.5
- <u><em>From the attached figure</em></u>
# There is a ray perpendicular to line
∴ The measure of the angle whose measure (225y/2)° is 90°
∴
- Multiply both sides by 2
∴ 225y = 180
- Divide both sides by 225
∴
* The value of y is 0.8