Question

question 11 of 50
the value of x is:
two triangles with angle and congruency marks
options: 33°, 66°, 48°

Explanation:

Step1: Calculate the unknown angle in the first triangle

In a triangle, the sum of interior angles is \(180^{\circ}\). Let the unknown angle in the first triangle be \(y\). Then \(y + 48^{\circ}+66^{\circ}=180^{\circ}\). So \(y = 180^{\circ}-(48^{\circ}+66^{\circ})=66^{\circ}\).

Step2: Use the angle - sum property for the second triangle

The second triangle is isosceles (two sides are equal). The sum of interior angles of a triangle is \(180^{\circ}\). So \(x + x+2x=180^{\circ}\). Combining like terms gives \(4x = 180^{\circ}\). Then \(x=\frac{180^{\circ}}{4}=45^{\circ}\). Wait, no. Wait, wait, wait. Wait, the first triangle: we can also note that \(x\) (from the first triangle) is equal to \(x\) (from the second triangle's non - \(2x\) angles) by some property (assuming similar or just using angle values). Wait, no, let's re - do.

First triangle: sum of angles \(x + 48^{\circ}+66^{\circ}=180^{\circ}\), so \(x=180^{\circ}-(48^{\circ}+66^{\circ}) = 66^{\circ}\). But wait, no, the second triangle: sum of angles \(x + x+2x=180^{\circ}\) (if it's an isosceles triangle with two equal angles \(x\)). But wait, no, looking at the first triangle: using the angle - sum property of a triangle (\(A + B + C=180^{\circ}\)), for the first triangle, \(x+48^{\circ}+66^{\circ}=180^{\circ}\), so \(x = 66^{\circ}\).

Answer:

\(66^{\circ}\)