1. The m < GKJ = 560m < GKH = 4x + 2 and m < JKH = 7x - 12 Solve for the measures of angles GKH and JKH. A ( 2 points) m<GKH= Box degrees m<JKH= Box degrees

Answer 1

To solve for the measures of angles GKH and JKH, we can set up the following equation:

m<GKJ + m<GKH + m<JKH = 180° (since the sum of angles in a triangle is 180°)

From the given information, we know that m<GKJ = 560°. Substituting this into the equation, we get:

560° + m<GKH + m<JKH = 180°

We also know that m<GKH = 4x + 2 and m<JKH = 7x - 12. Substituting these expressions into the equation, we get:

560° + (4x + 2) + (7x - 12) = 180°

Combining like terms, we can simplify the equation to:

11x + 550 = 180

Subtracting 550 from both sides, we get:

11x = -370

Dividing both sides by 11, we get:

x = -34

Now that we have the value of x, we can substitute it back into the expressions for m<GKH and m<JKH to find their specific values:

m<GKH = 4x + 2
m<GKH = 4(-34) + 2
m<GKH = -136 + 2
m<GKH = -134°

m<JKH = 7x - 12
m<JKH = 7(-34) - 12
m<JKH = -238 - 12
m<JKH = -250°

Therefore, the measures of angles GKH and JKH are:

m<GKH = -134°
m<JKH = -250°