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Learning Activities

Solve the following problems. Choose the letter of the correct answer. (Show your complete solutions)

1. The sum of all the sides of a STOP sign is 104 inches. A STOP sign is an octagon with all sides equal. How many inches does each side measure?
- A. 8 in
- B. 11 in
- C. 13 in
- D. 16 in

2. In triangle ABC, angle A and angle B each measure 70°. How many degrees are there in angle C?
- A. 40°
- B. 50°
- C. 60°
- D. 70°

3. The measures of the three angles of a quadrilateral are 49°, 58°, and 127°. What is the measure of the fourth angle?
- A. 116°
- B. 126°
- C. 54°
- D. 64°

4. Solve for the value of x in quadrilateral DEFG.
- D: (x + 40)°
- E: 130°
- F: (2x - 10)°
- G: 90°

- A. 40°
- B. 70°
- C. 50°
- D. 90°

5. If the lengths of the two sides of an isosceles triangle are 3 cm and 7 cm, then what must be the length of the third side?

Answer :

Answer:

1. C(13inches)

2. A(40°)

3. B(126°)

4. C(50°)

5. 7cm

Step-by-step explanation:

According To the Question,

1. Given, The sum of all the sides of a STOP sign is 104 inches. A STOP sign is Octagon with all sides equal.

Thus, Octagon has 8 equal side

So, Each Side Measure = 104/8 ⇔ 13inches

2. Given, In Triangle ABC, ∠A & ∠B each measure 70°

And, We Know Sum of all angles of a triangle is 180°.

Thus, ∠C = 180° - (∠A + ∠B) ⇔ 180°-140° ⇒ 40°

3. Given, The measures of the three angles of a quadrilateral are ∠A=49° ,∠B=58° & ∠C=127° .

And, We know sum of all angles of quadrilateral is 360°.

Thus, ∠D=360° - (∠A+∠B+∠C) ⇔ 360°-234° ⇒ 126°

4. Given, The measure of all the Four angles of a quadrilateral are ∠A=(x+40)°, ∠B=130°, ∠C=x° & ∠D=(2x-10)° .

And, We know sum of all the angles of quadrilateral is 360°.

Thus, ∠A+∠B+∠C+∠D = 360°

Put all the Values, we get

x+40+130+x+2x-10 = 360

4x+160 = 360

4x = 200 ⇔ 200/4 ⇒ 50°

5. Given, the length of the two sides of an isosceles triangle are 3cm and 7cm .

Now, in order to form a triangle the sum of any two side of a triangle is always greater than the third side of a triangle.

So, We have an isosceles triangle in which two sides is always equal & we have given two sides of 3cm & 7cm .

Assume, if third side be 3cm (First Side+Third side > Second side)

3+3 ⇒6cm which is not greater than 7cm(thus, the Triangle not possible if we assume 3cm as triangle's third side)

Hence, The other Side of Triangle Surely be 7 cm.

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Rewritten by : Barada

Step-by-step explanation:

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