Question

in the given figure, ∠acd = 16°. find the value of x. given x:y = 3:5 and ∠b = 160°. find the value of z.

Explanation:

Step1: Use exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In the triangle, if we consider the exterior angle of 160°, we have \(160^{\circ}=x + y\). Given \(x:y = 3:5\), let \(x = 3k\) and \(y = 5k\). Then \(160^{\circ}=3k + 5k\).

Step2: Solve for \(k\)

Combining like terms, we get \(160^{\circ}=8k\). So, \(k=\frac{160^{\circ}}{8}=20^{\circ}\).

Step3: Find \(x\) and \(y\)

Since \(x = 3k\), then \(x=3\times20^{\circ}=60^{\circ}\), and since \(y = 5k\), then \(y = 5\times20^{\circ}=100^{\circ}\).

Step4: Find \(z\)

\(z\) and the 160° angle are linear - pair angles. So \(z+160^{\circ}=180^{\circ}\), then \(z = 180^{\circ}-160^{\circ}=20^{\circ}\).

Answer:

\(x = 60^{\circ}\), \(y = 100^{\circ}\), \(z = 20^{\circ}\)