Question

One angle is twice its supplement increased by 102 degrees. Find the measures of the two supplementary angles.

Answer 1

One angle and its supplement give 180 when summed:

$\alpha+\beta = 180$

This implies that

$\alpha = 180-\beta$

we also know that

$\alpha = 2\beta+102$

So, we wrote $\alpha$ as $180-\beta$, but also as $2\beta+102$. So, the two expressions must equal each other, because they both equal $\alpha$:

$180-\beta = 2\beta+102 \iff 78=3\beta \iff \beta = 26$

This implies that $\alpha$ must complete $\beta$ so that they reach 180 together:

$\alpha = 180-\beta = 180-26 = 154$