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2 years ago

SV is an angle bisector of ∠RST. If m∠RSV = (3x + 5)° and m∠RST = (8x − 14)°, find x.

Mathematics

1 answer:

timama [110]2 years ago

4 0

First, let's define what an angle bisector is. Suppose you draw an angle labeled RST where the vertex is at point S, as shown in the attached picture. The angle bisector is a line segment that is drawn from the vertex S and extended outwards, such that it divides the angle into two equal parts. In this case, the angle bisector is line segment SV. The orange angle represents the total angle equal to (8x-14)°. The half of the angle, denoted as the red curve, represents (3x + 5)°. Th equation to be used is:

∠RST = 2×∠RSV
8x - 14 = 2(3x+5)
8x-14 = 6x + 10
8x - 6x = 10+14
2x = 24
x = 24/2
x = 12°

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Paula and Kawai shared $312 in the ratio of 6:7. How much money did each person get?

Maslowich

Answer:

Paula get $\$144$ and Kawai get $\$168$ .

Step-by-step explanation:

Given: Paula and Kawai shared $\$312$ in the ratio of $6:7$ .

To find: How much money did each person get?

Solution:

We have,

Paula and Kawai shared $\$312$ in the ratio of $6:7$ .

So, let Paula get $\$6x$ and Kawai get $\$7x$ .

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Therefore, Paula get $6\times 24=\$144$ , and Kawai get $7\times 24=\$168$ .

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