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I need help with this math hw its' in the image

I need help with this math hw its' in the image-example-1
User Esha
by
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1 Answer

23 votes
23 votes

Answer:

  • x = 7
  • y = 37

Explanation:

You want to know the values of x and y that make the angle measures consistent with the triangles being congruent in the given figure.

Congruence

The side markings show congruent triangles with corresponding vertices (and angles) ...

L (3x+24)° ⇔ P (8x -11)°

M 84° ⇔ Q 84°

N (2x +y)° ⇔ R (no marking)

Corresponding angles L and P have the same measure, so ...

3x +24 = 8x -11

35 = 5x . . . . . . . . add 11-3x

7 = x . . . . . . . . . divide by 5

The measures of these angles are ...

(3(7) +24)° = 45°

Angle sum theorem

The sum of the angles in each triangle is 180°, so the measure of angle N is found to be ...

L +M +N = 180°

45° +84° +N = 180°

N = 51°

This lets us find the value of y from ...

(2x +y)° = 51°

2(7) +y = 51

y = 37 . . . . . . . . subtract 14

The value of x is 7. The value of y is 37.

User Matt Culbreth
by
3.0k points