# In triangle PQR, the measure of angle P is 36 degrees. The measure of angle Q is five times the measure of angle R. How do you find the measurement of angle Q and the measurement of angle R?

Mar 31, 2017

#### Explanation:

"the sum of measures of these three angles of any triangle is invariably equal to the straight angle, also expressed as 180°"

From the problem we can write:

$Q = 5 R$

We can also write from Geometry, the sum of the three angles is 180 degrees, or:

$P + Q + R = 180$

We can substitute $36$ for $P$ and we can substitute $5 R$ for $Q$ and solve for $R$:

$36 + 5 R + R = 180$

$36 + 5 R + 1 R = 180$

$36 + \left(5 + 1\right) R = 180$

$36 + 6 R = 180$

$- \textcolor{red}{36} + 36 + 6 R = - \textcolor{red}{36} + 180$

$0 + 6 R = 144$

$6 R = 144$

$\frac{6 R}{\textcolor{red}{6}} = \frac{144}{\textcolor{red}{6}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} R}{\cancel{\textcolor{red}{6}}} = 24$

$R = 24$

Substituting $24$ for $R$ in the the equation for the relationship and calculating $Q$ gives:

$Q = 5 R$ becomes:

$Q = 5 \cdot 24$

$Q = 120$

Angle $Q$ is 120 degrees and angle $R$ is 24 degrees.