(a) What is the value of x in the figure given below if it is known that perimeter of the triangle is 86?

(b) Set up an equation in the following case and find the value of the unknown:
In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle be b in degrees. Remember that the sum of angles of a triangle is 180 degrees). [3 MARKS]

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Solution

(a) Concept: 1 Mark
(b) Setting up equation: 1 Mark
Solution: 1 Mark

(a) Since it is a triangle, the perimeter of a triangle is equal to the sum of all the sides of the triangle.

So, $x + (x + 3) + 41 = 86$

$\Rightarrow 2 x + 44 = 86$

$\Rightarrow 2 x = 42$

$\Rightarrow x = 21$ .

(b) Let the base angle be $b^{\circ}$
Let the vertex angle be $a^{\circ}$
In an isosceles triangle base angles are equal.
$∴ a^{\circ} + b^{\circ} + b^{\circ} = 180^{\circ}$

$2 b^{\circ} + b^{\circ} + b^{\circ} = 180^{\circ} \Rightarrow$ Given that vertex angle is twice the base angle.

$∴ 4 b^{\circ} = 180^{\circ}$

$b^{\circ} = (\frac{180}{4})^{\circ}$

$b^{\circ} = 45^{\circ}$

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