Question

Geometry
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Answer 1

Since triangle EFG is congruent to triangle RST, you can correspond the respective legs, hypotenuse, and angles to one another as all angles and side lengths are equal to each other.

Solving for x (right angles):

(4x+6) degrees = 90 degrees

4x=84

x = 21

Solving for y (acute angles):

(5y-2) degrees = 28 degrees

5y=30

y = 6

Solving for z (hypotenuses):

z+4 = 3z-8

z = 3z-12

-2z = -12

z = 6

Solving for angle F:

180 - (acute angle) - (right angle)

180 - 28 - 90 = 62 degrees

Note that 180 degrees is the total value you get when adding all angles up in all triangles regardless of shape.

Solving for side length ST:

Use z+4 and how z = 6

6+4 = 10

ST = 10

Hope this helps!

Answer 2

x=21, y=6, z=6

m ∡F=62°

ST=10

Explanation:

Given:

ΔEFG ≅ ΔRST

It means respective angle and side are equal.

For this question:

• m ∡E = m ∡R
• m ∡F = m ∡S
• m ∡G = m ∡T
• EF=RS
• FG=ST
• EG=RT

`\hrulefill`

Let's take the corresponding angles which value is given:

m ∡E = m ∡R = 90° Being right angle

it means

m ∡E=90°

• Substituting value

(4x+6)°=90°

• subtracting both side by 6.

4x=90°-6°

4x=84

• Dividing both side by 4.

x=84/4

x=21

Therefore, value of x is 21.

`\hrulefill`

Let's take the corresponding angles which value is given:

m ∡G = m ∡T

• Substitute value

(5y-2)°=28°

Adding both side by 2.

5y=28+2

5y=30

dividing both side by 5.

y=30/5=6

y=6

Therefore, value of y is 6.

`\hrulefill`

Let's take the corresponding side which value is given:

FG=ST

• Substitute value

3z-8=z+4

• Adding both side by 8

3z=z+4+8

3z=z+12

• Subtracting both side by z.

3z-z=12

2z=12

• dividing both side by 2.

z=12/2

z=6

Therefore, The value of z is 6.

`\hrulefill`

Now,

In Δ EFG

m ∡E+m ∡F+ m ∡G=180°

• Since sum of interior angle of a triangle is 180°
• Then substitute value

4x+6+m ∡F+28°=180°

since we know value of x.

4*21+6+ m ∡F+28°=180°

90°+ m ∡F+28°=180°

m ∡F+118°=180°

m ∡F=180°-118°

m ∡F=62°

Therefore, Value of m ∡F is 62°.

`\hrulefill`

Now,

ST= z+4

Substitute value of z

ST=6+4

ST=10

Therefore, ST is 10.