What is the measure of angle z in this figure?
1 answer:
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y = 90°
Solution:
The reference image for the answer is attached below.
The sum of opposite interior angles is equal to the exterior angles.
m∠BAC + m∠ACB = 110°
m∠BAC + 70° = 110°
m∠BAC = 110° – 70°
m∠BAC = 40°
m∠BAD + m∠DAC = 40°
x + x = 40°
2x = 40°
Divide by 2 on both sides of the equation.
x = 20°
In triangle DAC,
Sum of all the angles of a triangle = 180°
m∠DAC + m∠ACD + m∠CDA = 180°
20° + 70° + m∠CDA = 180°
90° + m∠CDA = 180°
m∠CDA = 180° – 90°
m∠CDA = 90°
∠CDA and y lies on the straight line. So they form a linear pair.
y + m∠CDA = 180°
y + 90° = 180°
y = 180° – 90°
y = 90°
The value of y is 90°.
For this case, the first thing we must do is define variables:
x: unknown number (1)
y: unknown number (2)
We now write the equations that model the problem:
their sum is 6.1:
their difference is 1.6:
Solving the system we have:
We add both equations:
Then, we look for the value of y using any of the equations:
Answer:
The numbers are:
x: unknown number (1)
y: unknown number (2)
We now write the equations that model the problem:
their sum is 6.1:
their difference is 1.6:
Solving the system we have:
We add both equations:
Then, we look for the value of y using any of the equations:
Answer:
The numbers are: