Question

question 3 (1 point)
140
130
a =
b =
blank 1:
blank 2:

Explanation:

Step1: Find the interior - angle related to 140°

The interior - angle adjacent to 140° is \(180 - 140=40^{\circ}\) since they are linear - pair angles.

Step2: Find the interior - angle related to 130°

The interior - angle adjacent to 130° is \(180 - 130 = 50^{\circ}\) as they are linear - pair angles.

Step3: Calculate angle a

In a triangle, the sum of interior angles is 180°. Let the third interior angle of the triangle be \(x\). We know two interior angles are 40° and 50°. So \(x=180-(40 + 50)=90^{\circ}\). Angle \(a\) and \(x\) are linear - pair angles, so \(a = 180-90=90^{\circ}\).

Step4: Calculate angle b

Angle \(b\) and the 50° interior angle of the triangle are vertical angles. Vertical angles are equal, so \(b = 50^{\circ}\).

Answer:

a = 90
b = 50