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?

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Answer 1 · 2017-03-31T11:46:55

"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:

$Q = 5R$

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 $5R$ for $Q$ and solve for $R$ :

$36 + 5R + R = 180$

$36 + 5R + 1R = 180$

$36 + (5 + 1)R = 180$

$36 + 6R = 180$

$-color(red)(36) + 36 + 6R = -color(red)(36) + 180$

$0 + 6R = 144$

$6R = 144$

$(6R)/color(red)(6) = 144/color(red)(6)$

$(color(red)(cancel(color(black)(6)))R)/cancel(color(red)(6)) = 24$

$R = 24$

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

$Q= 5R$ becomes:

$Q = 5 * 24$

$Q = 120$

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