Answer:
A. 78
Step-by-step explanation:
You want the measure of one base angle of an isosceles triangle when it is given as (6x+6)° while angle K is given as 2x°.
Angle relations
You don't need to solve any equations to determine the correct answer choice. You just need to understand the relationship between angles in an isosceles triangle.
The two base angles in an isosceles triangle are congruent, so neither can be more than 90°. (Eliminates choice C.)
The base angle at (6x+6) is more than 3 times angle K at (2x), so the base angle cannot be as little as 12.75. (Eliminates choices B and D.)
The only viable answer choice is A. 78°.
Solution
The sum of angles in any triangle is 180°. The two base angles in an isosceles triangle are the same measure, so we have ...
(6x +6)° +(6x +6)° +2x° = 180°
14x +12 = 180 . . . . . . . . . . . divide by °, collect terms
14x = 168 . . . . . . . . . . subtract 12
x = 12 . . . . . . . . . . divide by 14
∠D = (6x +6)° = (6·12 +6)° = 78°
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Additional comments
We are referring to the angle marked 2x° as "angle K" because Brainly doesn't like the word a.pex to show up in an answer.
We know triangle DKT is isosceles because the sides are marked with a single hash mark. The congruent base angles are opposite the congruent sides.
An altitude from K to segment DT would divide the triangle into two congruent right triangles, each with its half of angle K being x°. Then angles K/2 and T are complementary to that, so you could write ...
6x +6 +x = 90 ⇒ 7x = 84 ⇒ x = 12 ⇒ ∠D = 90° -12° = 78°
Once again, recognition that 6x+6 is somewhat greater than x means that angle D must be somewhat more than 45°. (The larger of two things is always greater than half their sum.)
