Answer:
15. x = 10 3/11
16. ∠Q = 75°
Step-by-step explanation:
<h3>15.</h3>
The two base angles of the isosceles triangle are congruent, so both are 180°-8x. The sum of those, together with the apex angle, will be 180°.
... 2(180 -8x) + (5x -67) = 180
... 360 -16x +5x -67 = 180 . . . . . eliminate parentheses
... -11x = -113 . . . . . subtract 293
... x = 113/11 = 10 3/11
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<em>Note on the solution</em>
This value of x makes the interior base angles of the triangle be 97 9/11°. The apex angle is then -15 7/11°. The solution is correct—all the angles add up properly—but the geometry cannot exist.
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<h3>16.</h3>
The approach is the same. The sum of the two congruent base angles and the apex angle is 180°.
... 2(2x+15) + x = 180
... 5x + 30 = 180
... x = (180 -30)/5 = 30
... (2x +15)° = (2·30 +15)° = 75° = angle Q
