Question

Triangle ABC is similar to triangle FGH. Given the following angle measures, find the missing angle measures.

m∠A = 22 degrees


m∠B = 75 degrees


m∠F = _____ degrees

m∠G = _____ degrees

m∠H = _____ degrees

m∠C = _____ degrees

Answer 1

Since triangle ABC is similar to triangle FGH, their angle measures are proportional. We can use the ratios of their angle measures to find the missing angle measures.

Let's call the missing angle measures x, y, z, and w, where x is m∠F, y is m∠G, z is m∠H, and w is m∠C.

From the given information, we have:

m∠A / m∠F = 22 / x

m∠B / m∠G = 75 / y

Since m∠A + m∠B + m∠C = 180 degrees, we can write:

w = 180 - (m∠A + m∠B)

m∠H / m∠C = z / w

Now we can use the ratios to find the missing angle measures:

x = 22 / (22 / x) = 22

y = 75 / (75 / y) = 75

z = m∠H / (m∠H / z) = m∠H

w = 180 - (22 + 75) = 83

So, the missing angle measures are:

m∠F = 22 degrees

m∠G = 75 degrees

m∠H = m∠H (unknown)

m∠C = 83 degrees