Question

1. there is a triangle abc, with angle at b being 80 degrees. there is a straight line cd, with angle between bc and cd being 147 degrees (the angle at c between bc and the lower part of cd is 147 degrees).

Explanation:

Step1: Find adjacent angle to 147°

Adjacent angles on a straight line sum to 180°. So, the angle at \( C \) inside the triangle is \( 180^\circ - 147^\circ = 33^\circ \).

Step2: Use triangle angle sum property

The sum of angles in a triangle is \( 180^\circ \). Let \( \angle A = x \). We know \( \angle B = 80^\circ \) and the angle at \( C \) (inside triangle) is \( 33^\circ \). So, \( x + 80^\circ + 33^\circ = 180^\circ \).

Step3: Solve for \( \angle A \)

Simplify the equation: \( x + 113^\circ = 180^\circ \). Subtract \( 113^\circ \) from both sides: \( x = 180^\circ - 113^\circ = 67^\circ \).

Answer:

The measure of \( \angle A \) is \( 67^\circ \)