Question

3. Triangle ABC has angle measures as shown.

Point A of the Triangle = X
Point B of the Triangle = ( x+2)
Point C of the Triangle = ( 6x+10)


(a) What is the value of x? Show your work.
(b) What is the measure of angle C? Show your work.

Answer 1

x = 21 and C = 136°.

Explanation:

(a) Sum of all the triangle = 180°.

∠A + ∠B + ∠C = 180°.

∠A= X, ∠B = x +2 , ∠C = 6x+10.

X + x + 2 + 6x + 10 = 180°.

8x + 12 = 180°.

8x = 168.

x = 21.

(b) The measure of angle C can be done by substituting the vale of x = 21.

6x + 10, x= 21.

=6 × 21 + 10

=136°.

Thus, the value of x = 21 and C = 136°.

Answer 2

The 3 inside angles of a triangle need to equal 180 degrees.

Add the 3 angles together to equal 180:

X + x+2 + 6x +10 = 180

Simplify:

8x + 12 = 180

Subtract 12 from each side:

8x = 168

Divide each side by 8:

x = 168 / 8

X = 21

a) x = 21

b) C = 6x+10

replace x with 21:

6(21) + 10 =

126 +10 = 136