Question

7
exterior angle theorem and
triangle sum theorem task cards
find ( mangle cab ).
(there is a triangle diagram with point c having an exterior angle of ( 110^circ ), side ab with angle at a labeled ( 2 + 6x ) and angle at b labeled ( 12x ))
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your answer
only give number do not write m angle abc. *
14
exterior angle theorem and
triangle sum theorem task cards

Explanation:

Step1: Apply Exterior Angle Theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles, so:
$$2 + 6x + 12x = 110$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$2 + 18x = 110$$
$$18x = 110 - 2$$
$$18x = 108$$
$$x = \frac{108}{18} = 6$$

Step3: Calculate $m\angle CAB$

Substitute $x=6$ into the angle expression:
$$m\angle CAB = 2 + 6(6)$$
$$m\angle CAB = 2 + 36$$

Answer:

38