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Anestetic [448]
3 years ago
13

Find the measure of angle 1

Mathematics
2 answers:
Lubov Fominskaja [6]3 years ago
8 0
In ∆FDH, there are two slash marks in two of its legs. This indicates that this triangle is isosceles. If a triangle is isosceles, then it will have two congruent sides and therefore have two congruent angles.

In ∆FDH, angle D is already given to us as the measure of 80°. We can find out the measure of the other angles of this triangle by using the equation:

80 + 2x = 180

Subtract 80 from both sides of the equation.

2x = 100

Divide both sides by 2.

x = 50

This means that angle F and angle H in ∆FDH both measure 50°.

Now, moving over to the next smaller triangle in the picture is ∆DHG. In this triangle, there are also two legs that are congruent which once again indicates that this triangle is isosceles.

First, we have to solve for angle DHG and we do that by using the information obtained from solving for the angles of the other triangle.

**In geometry, remember that two or more consecutive angles that form a line will always be supplementary; the angles add up to 180°.**

In this case angle DHF and angle DHG are consecutive angles which form a linear pair. So, we can use the equation:

Angle DHF + Angle DHG = 180°

50° + Angle DHG = 180°.

Angle DHG = 130°.

Now that we know the measure of one angle in ∆DHG, we can use the same method as the previous step for solving the missing angles. Use the equation:

130 + 2x = 180

2x = 50

x = 25

The other two missing angles of ∆DHG are 25°. This means that the measure of angle 1 is also 25°.

Solution: 25°
Alexandra [31]3 years ago
5 0
Find the measure of angle 1

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<u>Question 6</u>

1) \overline{AB} \cong \overline{BD}, \overline{CD} \perp \overline{BD}, O is the midpoint of \overline{BD}, \overline{AB} \cong \overline{CD} (given)

2) \angle ABO, \angle ODC are right angles (perpendicular lines form right angles)

3) \triangle ABO, \triangle CDO are right triangles (a triangle with a right angle is a right triangle)

4) \overline{BO} \cong \overline{OD} (a midpoint splits a segment into two congruent parts)

5) \triangle ABO \cong \triangle CDO (LL)

<u>Question 7</u>

1) \angle ADC, \angle BDC are right angles), \overline{AD} \cong \overline{BD}

2) \overline{CD} \cong \overline{CD} (reflexive property)

3) \triangle CDA, \triangle CDB are right triangles (a triangle with a right angle is a right triangle)

4) \triangle ADC \cong \triangle BDC (LL)

5) \overline{AC} \cong \overline{BC} (CPCTC)

<u>Question 8</u>

1) \overline{CD} \perp \overline{AB}, point D bisects \overline{AB} (given)

2) \angle CDA, \angle CDB are right angles (perpendicular lines form right angles)

3) \triangle CDA, \triangle CDB are right triangles (a triangle with a right angle is a right triangle)

4) \overline{AD} \cong \overline{DB} (definition of a bisector)

5) \overline{CD} \cong \overline{CD} (reflexive property)

6)  \triangle ADC \cong \triangle BDC (LL)

7) \angle ACD \cong \angle BCD (CPCTC)

8 0
2 years ago
If There was a game and the game cost 130$ and you only have 53$ what would you do to find the amswer​
anygoal [31]

Answer:

130-53= $77

Step-by-step explanation:

6 0
3 years ago
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Which expression can be used to convert 80 dollars (USD) to Australian dollars (aud) 1 USD=1.0343 AUD 1 AUD 0.9668 USD
lesya692 [45]

Answer: 1\ \text{USD}\equiv 1.35\ \text{AUD}

Step-by-step explanation:

1 USD is equivalent to 1.35 AUD

Therefore, 80 USD is equivalent to

\Rightarrow 80\ \text{USD}\equiv 80\times 1.35\\\\\Rightarrow 108\ \text{AUD}

4 0
3 years ago
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