m∠WYX=(2x−1)° and m∠WYZ=(4x+1)°. If ∠WYX and ∠WYZ are complementary, what is the measure of each angle?

Mathematics

1 answer:

Neko [114]4 years ago

5 0

We are given : m∠WYX=(2x−1)° and m∠WYZ=(4x+1)°.

∠WYX and ∠WYZ are complementary.

We know, sum of complementary angles is = 90°.

So, we need to add ∠WYX and ∠WYZ and set it equal to 90°.

m∠WYX + m∠WYZ = 90°.

Plugging values of ∠WYX and ∠WYZ in the above equation, we get

(2x−1)° + (4x+1)° = 90°.

Removing parentheses from both sides,

2x-1 + 4x+1 =90.

Combining like terms,

2x+4x= 6x and -1+1 =0

6x +0 =90.

6x=90.

Dividing both sides by 6.

6x/6 =90/6

x= 15.

Plugging value of x=15.

m∠WYX=(2x−1)° = 2*15 -1 = 30 -1 =29

m∠WYZ=(4x+1)° = 4*15 +1 = 60+1 = 61.

Therefore, ∠WYX=29° and ∠WYZ=61°.

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The exterior angles of a pentagon are (m+5)°, (2m+3)°, (3m+2)°, (4m+1)° and (5m+4)° respectively. Find the measure of each angle

olga nikolaevna [1]

Answer:

Step-by-step explanation:

Sum of exterior angles of any polygon =360°

Sum of exterior angles of polygon = 360°

m + 5 + 2m + 3 + 3m + 2 + 4m + 1 + 5m + 4 = 360

m + 2m + 3m + 4m + 5m + 5 + 3 + 2 + 1 + 4 = 360 {Combine like terms}

15m + 15 = 360 {Subtract 15 from both sides}

15m = 360 - 15

15m = 345 {Divide both sides by 15}

m = 345/15

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5m + 4 = 5*23 + 4 = 115 + 4 = 119°

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3 years ago

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In triangle xyz, z2 = x2 + y2. triangle xyz has sides x, qy, z opposite to the corresponding vertices x, y, z which equation is

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${\text{In triangle XYZ}},{\text{ square of one side is equal to the sum of squares of other two sides, }} \hfill \\ {\text{,i}}{\text{.e}}{\text{., if triangle XYZ has sides of measure }}x\,{\text{unit, }}y\,{\text{unit and }}z\,{\text{unit}} \hfill \\ {\text{opposite to the corresponding vertices }}X,{\text{ }}Y\,{\text{and }}Z\,{\text{respectively, then}} \hfill \\ {z^2} = {x^2} + {y^2} \hfill \\ {\text{Since, the given triangle satisfying the condition of Pythagoras theorem, }} \hfill \\{\text{thus, the given triangle would be a right angled triangle and thereby the measure}} \hfill \\{\text{of one angle of triangle will be a right angle say at vertex Z}}{\text{.}} \hfill \\\Rightarrow m\left( {\angle Z} \right) = 90^\circ \hfill \\\Rightarrow m\left( {\angle XZY} \right) = 90^\circ \hfill \\{\text{Thus,the measure of angle XZY is equal to }}90{\text{ }}degrees. \hfill \\$