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2 years ago

What is the measure of angle VYZ

Mathematics

1 answer:

irakobra [83]2 years ago

7 0

Answer:

$\boxed{\sf C. \ 161 ^{ \circ}}$

Step-by-step explanation:

Opposite angles are also congruent angles, meaning they are equal or have the same measurement.

$\sf \implies \angle VYZ = \angle WYT \\ \\ \sf \implies(8x + 1) ^{ \circ} = (9x - 19)^{ \circ} \\ \\ \sf \implies 8x^{ \circ} + 1^{ \circ} = 9x^{ \circ} - 19^{ \circ} \\ \\ \sf \implies 8x^{ \circ} - 9x^{ \circ} + 1^{ \circ} = - 19^{ \circ} \\ \\ \sf \implies - x^{ \circ} = - 19^{ \circ} - 1^{ \circ} \\ \\ \sf \implies \cancel{ -} x^{ \circ} = \cancel{- }20^{ \circ} \\ \\ \sf \implies x^{ \circ} = 20^{ \circ}$

$\therefore$

$\sf \implies \angle VYZ =(8x + 1) ^{ \circ} \\ \\ \sf \implies \angle VYZ =(8 \times 20 + 1) ^{ \circ} \\ \\ \sf \implies \angle VYZ =( 160+ 1) ^{ \circ} \\ \\ \sf \implies \angle VYZ =161 ^{ \circ}$

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<h2>The missing measures of the angles are:</h2>

$m\angle 1= 60^{\circ}\\\\m\angle 2= 39^{\circ}\\\\m\angle 3= 21^{\circ}\\\\m\angle 4 = 39^{\circ}\\\\m\angle 5 = 21^{\circ}$

Given:

$m\angle Z = 138^{\circ}$

Note the following:

An equilateral triangle has all its three angles equal to each other. Each angle = $60^{\circ}$ .

This implies that, since $\triangle WXY$ is equilateral, therefore, $m\angle Y = m\angle XWY = m\angle XYW = 60^{\circ}$

Base angles of an isosceles triangle are congruent to each other.

This implies that, since $\triangle WZY$ is isosceles, therefore, $m\angle 3 = \angle 5$

Applying the above stated, let's find the measure of each angle:

Find $m\angle 1$

$m\angle 1 = 60^{\circ}$ (an angle in an equilateral triangle equals 60 degrees)

Find $m\angle 2$

$m\angle 2 = 60 - m \angle 3$

$m\angle 2 = 60 -\frac{1}{2}(180 - 138)$ $(Note: \frac{1}{2}(180 - 138) = 1 $ base $ angle $ of $ \triangle WZY)$

$m\angle 2 = 60 -21\\\\m\angle 2 = 39^{\circ}$

Find $m\angle 3$ and $m\angle 5$ (base angles of isosceles triangle WZY)

$m\angle 3 = \frac{1}{2}(180 - 138) (1 $ base $ angle $ of $ \triangle WZY)$

$m\angle 3 = \frac{1}{2}(42) \\\\m\angle3 = 21^{\circ}$

$m\angle3 = m\angle 5$ (base angles of isosceles triangle are congruent)

Therefore,

$m\angle5 = 21^{\circ}$

Find $m\angle 4$

$m\angle 4 = 60 - m\angle 5$

Substitute

$m\angle 4 = 60 - 21\\\\m\angle 4 = 39^{\circ}$

The missing measures of the angles are:

$m\angle 1= 60^{\circ}\\\\ m\angle 2= 39^{\circ}\\\\m\angle 3= 21^{\circ}\\\\m\angle 4 = 39^{\circ}\\\\m\angle 5 = 21^{\circ}$

Learn more here:

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