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Find the measure of indicated angles

Find the measure of indicated angles-example-1
User Seoras
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The values of the marked angles are:

11) ∠1 = 81⁰ ∠4 = 74⁰

∠2 = 24⁰ ∠5 = 24⁰

∠3 = 105⁰

12) ∠1 = 76⁰ ∠3 = 76⁰

∠2 = 104⁰ ∠4 = 80⁰

What are similar triangles?

In similar triangles, corresponding angles are equal, meaning that each angle in one triangle has a corresponding angle in the other triangle with the same measure.

11) The two triangles in the figures are similar.

∠4 = 74⁰(corresponding ∠s of similar ∆)

∠3 + 75 = 180⁰( linear ∠s)

∠3 = 180 - 75

∠3 = 105⁰

∠2 + 156 = 180(linear ∠s)

∠2 = 180 - 156

= 24⁰

∠5 = 24⁰(corresponding ∠s of similar ∆)

75 + 24 + ∠1 = 180(sum of int. ∠s of a ∆)

99 + ∠1 = 180

∠1 = 180 - 99 = 81⁰

12) 16x + 20 + 21x - 25 = 180(adjacent angles of quadrilateral

37x = 180 + 5

37x = 185

x = 185/37 = 5

21x -25 = 21(5) -25

= 105 - 25 = 80⁰

16x + 20 = 16(5) + 20

= 80 + 20 = 100⁰

∠4 = 80⁰( corresponding ∠s of similar ∆)

∠1 + 80 + 24 = 180(∠s in a ∆)

∠1 + 104 = 180

∠1 = 180 - 104 = 76⁰

∠1 + ∠2 = 180(linear ∠s)

∠2 = 180 - 76 = 104⁰

∠1 = ∠3 = 76⁰

User Raveturned
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