Question

1. look at the triangle below.

the smallest angle is ( x ), the largest angle is three times the smallest, and angle ( c ) is twice the smallest angle. in ( \triangle abc ), find the measure of angle ( b ).
options: ( 90^circ ), ( 30^circ ), (a blurred option), ( 100^circ )

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(x + 2x + 3x = 180^\circ\).

Step2: Solve for \(x\)

Combine like terms: \(6x = 180^\circ\). Divide both sides by 6: \(x = \frac{180^\circ}{6} = 30^\circ\).

Step3: Find angle B

Angle B is \(3x\), so substitute \(x = 30^\circ\): \(3\times30^\circ = 90^\circ\).

Answer:

The measure of angle B is \(90^\circ\).