Question

Classify each pair of numbered angles. Drag and drop the descriptions into the boxes to correctly classify each pair of numbered angles. Each description may be used more than once. Two lines intersect. The largest angle has the equation (3x minus 52) degrees to define it and the second to largest angle has the equation (2x plus 2) degrees to define it. A straight line with another line coming out of it at an angle. The largest angle has the equation (10x minus 20) degrees to define it and the smaller angle has the equation (6x plus 8) degrees to define it.

Answer 1

(i) Pairs of neighboring angles are supplementary and opposite angles have the same measure.

(ii) The two angles formed by a line coming out of another line are supplementary.

How to analyze pairs of angles

(i) When two straight lines pass through each other, then two pairs of opposite angles are constructed. A pair with angles of $(3\cdot x + 52)^{\circ}$ and another pair with angles of $(2\cdot x + 2)^{\circ}$, each pair of angles with different measures are supplementary.$\blacksquare$

(ii) When a straight line comes out of another straight line, from a point distinct to any endpoint of the former, then we construct two supplementary angles. The largest angle has a value of $(10\cdot x + 20)^{\circ}$, whereas the smaller one has a value of $(6\cdot x + 8)^{\circ}$. $\blacksquare$

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