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Alinara [238K]
2 years ago
9

N a circle graph displaying the most popular juice sold to students in the school cafeteria, the ratio of apple juice boxes to t

otal juice boxes sold is 34
. What is the angle measure of the
Mathematics
1 answer:
ivolga24 [154]2 years ago
4 0
Sorry don’t focus on my comments because it say to answer two people comment before i ask questions.
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What is the area of the base of the cone?
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Which graph represents a function with the initial value of 1/2<br><br> Graph 2
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Triangle WXY is isosceles. ∠YWX and ∠YXW are the base angles. YZ bisects ∠WYX. m∠XYZ = (15x)°. m∠YXZ = (2x + 5)°. What is the me
DiKsa [7]

Answer:

Option D is correct.

The measure of \angleWYX = 150^{\circ}

Step-by-step explanation:

\triangle WXY is isosceles  and \angle YWX and \angle YXW are base angles.

Isosceles Triangle:

A triangle with two equal sides, and two congruent base angles that means the angles are equal

By the definition, the base angles are equal i.e, m\angle YWX=m\angle YXW

Since, YZ bisects m\angle WYX

Angle Bisector theorem: An angle bisector is a line or ray that divides an angle into two equal angles

then, \angle WYX =2\angle XYZ or

Substitute the value of \angle XYZ=(15x)^{\circ} ;

\angle WYX =2(15x)^{\circ} = (30x)^{\circ}

The sum of measures of these three angles of  triangle WXY is equal to the 180 degree.

In triangle WXY we have;

\angle YXW+\angle WYX+\angle YWX=180^{\circ}

Substitute the value of m\angle YWX=m\angle YXW=(2x+5)^{\circ} and \angle WYX=(30x)^{\circ} in above formula:

2\angle YXW+30x=180^{\circ} or

2\cdot(2x+5)+30x=180^{\circ}

Simplify:

4x+10+30x=180^{\circ}

Combine like terms ;

34x+10^{\circ}=180^{\circ} or

34x=170^{\circ}

Simplify;

x= \frac{170}{34} =5^{\circ}

Substitute the value of x in  \angle WYX;

\angleWYX = (30x)^{\circ} = 30 \cdot 5 = 150^{\circ}

Therefore, the measure of \angleWYX = 150^{\circ}






7 0
3 years ago
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