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sasho [114]
3 years ago
7

Find the values of x, y, and z. The diagram is not to scale.

Mathematics
2 answers:
adoni [48]3 years ago
7 0
Start by finding x.

All triangles have the property that their angles add up to 180°.

So you know from the diagram that:
36 + 63 + x = 180
Solve for x.

Similarly, looking at the larger triangle that holds the two smaller triangles, try solving for y. The top of the triangle is made up of 13° and 36°. 13 + 36 = 49.
So since we know the angles have to add up to 180°, we can solve for y in the equation:
63 + 49 + y = 180
Solve for y.

Lastly, solve for z using the same process! If you have any questions, just comment here. You've got this!
Kruka [31]3 years ago
5 0

we know that

The sum of the internal angles in the triangle must be 180 degrees

see the attached figure with letters to better understand the problem

Step 1

<u>Find the measure of the angle x</u>

In the triangle ABC

63\°+36\°+x\°=180\°

solve for x

99\°+x\°=180\°

x\°=180\°-99\°

x=81\°

therefore

<u>the answer Part a)  is</u>

the measure of angle x is 81\°

Step 2

<u>Find the measure of the angle z</u>

we know that

x+z=180\° --------> by supplementary angles

substitute the value of x

81\°+z=180\°

z=180\°-81\°

z=99\°

therefore

<u>the answer Part b)  is</u>

the measure of angle z is 99\°

Step 3

<u>Find the measure of the angle y</u>

In the triangle ACD

13\°+z\°+y\°=180\°

solve for y

13\°+99\°+y\°=180\°

112\°+y\°=180\°

y\°=180\°-112\°

y\°=68\°

therefore

<u>the answer Part c)  is</u>

the measure of angle y is 68\°

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