Questions: Segments and Angles Solving an equation involving complementary or supplementary angles In the figure below, m angle 1=(x-5)° and m angle 2=4x°. Find the angle measures.

Solution Steps

Since angles 1 and 2 form a straight line, they are supplementary. This means their measures add up to 180 degrees.

Given: $$m \angle 1 = (x - 5)^\circ$$ $$m \angle 2 = 4x^\circ$$ Since they are supplementary: $$(x - 5) + 4x = 180$$

Combine like terms: $$5x - 5 = 180$$ Add 5 to both sides: $$5x = 185$$ Divide by 5: $$x = 37$$

Substitute $x = 37$ back into the expressions for the angles: $$m \angle 1 = (37 - 5)^\circ = 32^\circ$$ $$m \angle 2 = 4 \times 37^\circ = 148^\circ$$

Final Answer