Question

in an isosceles triangle, one angle is 28° more than twice the measure of one of the equal angles. find the measure of each angle.
° (smaller angle)
° (smaller angle)
° (larger angle)
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Explanation:

Step1: Let the measure of each equal angle be $x$.

Let the larger angle be $y$. Given that $y = 2x+28$.

Step2: Use the angle - sum property of a triangle.

The sum of the interior angles of a triangle is $180^{\circ}$. So, $x + x + y=180$. Substitute $y = 2x + 28$ into the equation: $x+x+(2x + 28)=180$.

Step3: Simplify the equation.

Combine like - terms: $4x+28 = 180$.

Step4: Solve for $x$.

Subtract 28 from both sides: $4x=180 - 28=152$. Then divide both sides by 4: $x=\frac{152}{4}=38$.

Step5: Find the measure of the larger angle $y$.

Substitute $x = 38$ into $y = 2x+28$. So, $y=2\times38 + 28=76+28 = 104$.

Answer:

38
38
104