A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -4. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -3) and (2, -5) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = -\(\frac{1}{2}\)x - 4

You need to find the value of a so solve the first equation in terms of y:

-6a + y = -3
y = -3 + 6a

then substitute the result (-3 - -6a) into the second equation:

6a + 5(-3 + 6a) = 7
6a + (5 x -3) + (5 x 6a) = 7
6a - 15 + 30a = 7
6a + 30a = 7 + 15
36a = 22
a = \( \frac{22}{36} \)
a = \(\frac{11}{18}\)

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 41° - 53° = 86°

So, d° = 53° + 86° = 139°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 41° = 139°

The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 63° - 69° = 48°