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3 years ago

YM is a median of the triangle below. XM = 2x + 2 and ZM = 4x - 8. What 5 points

Mathematics

1 answer:

LenaWriter [7]3 years ago

4 0

Answer:

Option A: 12

Step-by-step explanation:

From the image of the triangle given, we can see that:

XM = ZM

We are given that:

XM = 2x + 2 and ZM = 4x - 8

Thus;

2x + 2 = 4x - 8

Rearrange to get;

4x - 2x = 8 + 2

2x = 10

x = 10/2

x = 5

Thus, XM = 2(5) + 2

XM = 12

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Answer:

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Step-by-step explanation:

Incomplete question:

$\angle CBD = 53^\circ$

$\angle CAB = 35^\circ$

$AB = 75$

See attachment for complete question

Required

Determine the equation to find x

First, is to complete the angles of the triangle (ABC and ACB)

$\angle ABC + \angle CBD = 180$ --- angle on a straight line

$\angle ABC + 53= 180$

Collect like terms

$\angle ABC =- 53+ 180$

$\angle ABC =127^\circ$

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$\angle ACB + 127 + 35 = 180$

Collect like terms

$\angle ACB =- 127 - 35 + 180$

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Apply sine rule

$\frac{\sin A}{a} = \frac{\sin B}{b}$

In this case:

$\frac{\sin ACB}{AB} = \frac{\sin CAB}{x}$

This gives:

$\frac{(\sin 18^\circ)}{75} = \frac{(\sin 35^\circ)}{x}$

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