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spin [16.1K]
2 years ago
8

Hey everyone i was trying to setup this problem but I’m stuck can someone tell me setup for number 15 and 16 explain if you can

:)

Mathematics
1 answer:
STatiana [176]2 years ago
5 0

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

_____

<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.

_____ _____

<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

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