Question

An architect designs two similar triangular patios. The first patio has angle measures of (x + 10)°, (y + 15)°, and 70°. The second patio has angle measures of (x + 20)°, 50°, and 60°. Find the values of x and y.

Answer 1

Given:

An architect designs two similar triangular patios.

The first patio has angle measures of (x + 10)°, (y + 15)°, and 70°.

The second patio has angle measures of (x + 20)°, 50°, and 60°.

To find:

The values of x and y.

Solution:

We know that, corresponding angles of similar triangles are equal. So, the value of (x + 20)° must be 70°.

$x+20=70$

$x=70-20$

$x=50$

The value of x is 50.

Now,

$(x+10)^\circ=(50+10)^\circ$

$(x+10)^\circ=(60)^\circ$

So, remaining angles must be equal, i.e., (y + 15)° and 50° are equal.

$y+15=50$

$y=50-15$

$y=35$

Therefore, the values of x and y are 50 and 35 respectively.

Answer 2

The values of x and y are 50 and 35 respectively.

The corresponding angles of similar triangles are equal. Therefore,

The first patio angles are:

x + 10

y + 15

70°

The second patio angles are ;

x + 20

50°

60°

Therefore,

x + 20 = 70

x = 70 - 20

x = 50

y + 15 = 50

y = 50 - 15

y = 35

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