Question

One angle of a triangle has a measure of 66. The measure of the third angle is 57 more than half the measure of the second angle. The sum of the angle measures of a triangle is 180

Answer 1

So let's say that the second angle is x.

Then we can say that the third angle is $\frac{1}{2}x+57$.

So then we have three angles:

1) 66°

2) x°

3) ($\frac{1}{2}x+57$)°

So then we can add these together and solve for x by setting it equal to the total degrees left in the triangle after subtracting the known angle:

$x+\frac{1}{2}x+57=114$

$\frac{3}{2}x+57=114$

$\frac{3}{2}x=57$

$\frac{2}{3}*\frac{3}{2}x=57*\frac{2}{3}$

$x=\frac{114}{3} =38$

So now we know that the measure of the second angle is 38°. So then we can use this value to solve for the third angle:

$\frac{1}{2}(38) +57=76$

So the values of the angles are:

1) 66°

2) 38°

3) 76°

Answer 2

Answer:

The measure of the second ans third angles is 38° and 76° respectively.

Step-by-step explanation:

Let angles of the triangle be  : x,y,z

x =  First angle of the triangle = 66°

y = Second angle of the triangle

z = Third angle of the triangle

According to question:

$z = 57 +\frac{1}{2}y$

$x+y+z=180^o$ (Angle sum property of triangle)

$66^o+y+57 +\frac{1}{2}y=180$

y = 38°

z = 76°