Question

A home has a triangular backyard. The second angle of the triangle is 4º more than the

Answer 1

Answer:

31, 114 and 35

Step-by-step explanation:

I set up the equation as such:

(3x + 21) + (x + 4) + x = 180

then I combined like terms:

5x + 25 = 180

And then solving for x I get:

5x = 155

x = 31

And then plugged the solved x value into the terms to give:

(3(31) + 21) = 114

(31 + 4) = 35

alongside the found angle of 31.

Answer 2

Answer:

$31^{\circ}, 35^{\circ}, 114^{\circ}$

Step-by-step explanation:

Let the first angle be $x$. Then, the second angle is $(x+4)^{\circ}$ and the third angle is $(3x+21)^{\circ}$.

We know that the sum of the angles in a triangle will always be $180^{\circ}$. So, we want to solve the equation for x: $(x)+(x+4)+(3x+21)=180$.

Combining like terms on the left side gives $5x+25=180$.

Subtracting $25$ from both sides gives $5x=155$.

Dividing both sides by $5$ gives $x=31$.

So, the first angle is $31^{\circ}$.

The second angle is $x+4=31+4=35$, so the second angle is $35^{\circ}$.

The third angle is $3x+21=3(31)+21=93+21=114$, so the third angle is $114^{\circ}$.

So, the angles are $\boxed{31^{\circ}, 35^{\circ}, 114^{\circ}}$ and we're done!

The check that these angles work is left as an exercise to the reader.