Question

try on your own: solve for x. 1. find x if the base angle of an isosceles triangle are 38 degrees and 7x + 17 2. two sides of an equilateral angle are 15x - 8 and 13x + 12, solve for x. 3. triangle image with 60° and 2x

Explanation:

Step1: Set base angles equal

$7x + 17 = 38$

Step2: Isolate term with x

$7x = 38 - 17$
$7x = 21$

Step3: Solve for x

$x = \frac{21}{7}$
$x = 3$

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Step1: Set sides of equilateral figure equal

$15x - 8 = 13x + 12$

Step2: Isolate terms with x

$15x - 13x = 12 + 8$
$2x = 20$

Step3: Solve for x

$x = \frac{20}{2}$
$x = 10$

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Step1: Identify equilateral triangle

The left triangle has 2 equal sides and a $60^\circ$ angle, so it is equilateral. All angles are $60^\circ$, and the marked segment creates an isosceles triangle on the right with one angle $= 180^\circ - 90^\circ - 60^\circ = 30^\circ$.

Step2: Set base angles of isosceles triangle equal

The right triangle has two equal sides, so its base angles are equal: $2x = 30$

Step3: Solve for x

$x = \frac{30}{2}$
$x = 15$

Answer:

1. $x = 3$
2. $x = 10$
3. $x = 15$