Question

find the value of x.
(there is a triangle with a 65° angle and two equal sides marked, and the angle at the base is x°)
enter the correct number in the box.
show hints
x =
(there is a number pad with numbers 7,8,9,+, 4,5,6,-, 1,2,3,×, 0,.,, ÷ and a cursor on 8)

Explanation:

Step1: Recognize the triangle type

Since two sides of the triangle are equal (marked with the same tick - marks), it is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let the two equal angles be \(y\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). So, \(65^{\circ}+y + y=180^{\circ}\).
Simplify the equation: \(65^{\circ}+2y = 180^{\circ}\).
Subtract \(65^{\circ}\) from both sides: \(2y=180^{\circ}- 65^{\circ}=115^{\circ}\).
Divide both sides by 2: \(y=\frac{115^{\circ}}{2}=57.5^{\circ}\).

Answer:

\(x = 57.5\)