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marin [14]
3 years ago
11

.Find the unknown angles in each of the following figures and mention the property used​

Mathematics
1 answer:
forsale [732]3 years ago
7 0

Answer/Step-by-step explanation:

a. Angle y is vertically opposite the angle that measures 80°. Vertically opposite angles are said to be equal to each other, therefore, y = 80°

x + y + 50° = 180° (sum of angles in a ∆)

x + 80° + 50° = 180 (substitution)

x + 130° = 180°

x = 180° - 130° (subtracting 130 from each side)

x = 50°

b. x + 50° = 120° (sum of the 2 opposite interior angles in a ∆ = the exterior angle of the ∆)

x = 120 - 50 (subtracting 50 from each side)

x = 70°

y + x + 50° = 180° (sum of angles in a ∆)

y + 70° + 50 = 180° (substitution)

y + 120° = 180°

y = 180 - 120 (subtracting 120 from each side)

y = 60°

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Suppose that MNO is isosceles with base NM. Suppose also that =m∠N+4x7° and =m∠M+2x29°. Find the degree measure of each angle in
chubhunter [2.5K]

Answer:

m∠N = 51°

m∠M = 31°

m∠O = 98°

Step-by-step explanation:

It is given that ΔMNO is an isosceles triangle with base NM.

m∠N = (4x + 7)° and m∠M = (2x + 29)°

By the property of an isosceles triangle,

Two legs of an isosceles triangle are equal in measure.

ON ≅ OM

And angles opposite to these equal sides measure the same.

m∠N = m∠M

(4x + 7) = (2x + 29)

4x - 2x = 29 - 7

2x = 22

x = 11

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m∠M = (2x + 9)° = 31°

m∠O = 180° - (m∠N + m∠M)

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3 years ago
What are the coordinates of D’ after a dilation with a scale factor of 2?
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(In picture) “Explain how you know you know using proportional lengths”
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9514 1404 393

Answer:

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Step-by-step explanation:

If GH║FE, then ∆DEF ~ ∆DHG.

In similar triangles, corresponding sides have the same ratios.

The ratios of corresponding sides are ...

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Corresponding sides are proportional. Angle D is congruent to itself, so ∆DEF ~ ∆DHG by the SAS similarity postulate. Angles DGH and DFE are therefore congruent and GH║FE.

7 0
3 years ago
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