Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To find the measures of all the angles in a parallelogram where the ratio of two adjacent angles is given as [tex]\( 7:17 \)[/tex], follow these steps:
1. Understand the properties of a parallelogram:
- Adjacent angles in a parallelogram add up to [tex]\(180^\circ\)[/tex].
- Opposite angles in a parallelogram are equal.
2. Set up the relationship with a variable:
- Let's represent the two adjacent angles as [tex]\(7x\)[/tex] and [tex]\(17x\)[/tex], where [tex]\(x\)[/tex] is a common multiple.
3. Formulate the equation based on the property of adjacent angles:
- According to the property of adjacent angles in a parallelogram:
[tex]\[ 7x + 17x = 180^\circ \][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Combine like terms:
[tex]\[ 24x = 180^\circ \][/tex]
- Divide both sides by 24 to find [tex]\(x\)[/tex]:
[tex]\[ x = \frac{180}{24} \][/tex]
5. Calculate the value of [tex]\(x\)[/tex]:
- [tex]\[ x = 7.5 \][/tex]
6. Determine the measures of the angles:
- Calculate the first angle:
[tex]\[ \text{First angle} = 7x = 7 \times 7.5 = 52.5^\circ \][/tex]
- Calculate the second angle:
[tex]\[ \text{Second angle} = 17x = 17 \times 7.5 = 127.5^\circ \][/tex]
7. Assign these measures to corresponding angles in the parallelogram:
- Since opposite angles in a parallelogram are equal, the other two angles will also be [tex]\(52.5^\circ\)[/tex] and [tex]\(127.5^\circ\)[/tex].
Therefore, the measures of all the angles in the parallelogram are:
[tex]\[ 52.5^\circ, 127.5^\circ, 52.5^\circ, 127.5^\circ \][/tex]
1. Understand the properties of a parallelogram:
- Adjacent angles in a parallelogram add up to [tex]\(180^\circ\)[/tex].
- Opposite angles in a parallelogram are equal.
2. Set up the relationship with a variable:
- Let's represent the two adjacent angles as [tex]\(7x\)[/tex] and [tex]\(17x\)[/tex], where [tex]\(x\)[/tex] is a common multiple.
3. Formulate the equation based on the property of adjacent angles:
- According to the property of adjacent angles in a parallelogram:
[tex]\[ 7x + 17x = 180^\circ \][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Combine like terms:
[tex]\[ 24x = 180^\circ \][/tex]
- Divide both sides by 24 to find [tex]\(x\)[/tex]:
[tex]\[ x = \frac{180}{24} \][/tex]
5. Calculate the value of [tex]\(x\)[/tex]:
- [tex]\[ x = 7.5 \][/tex]
6. Determine the measures of the angles:
- Calculate the first angle:
[tex]\[ \text{First angle} = 7x = 7 \times 7.5 = 52.5^\circ \][/tex]
- Calculate the second angle:
[tex]\[ \text{Second angle} = 17x = 17 \times 7.5 = 127.5^\circ \][/tex]
7. Assign these measures to corresponding angles in the parallelogram:
- Since opposite angles in a parallelogram are equal, the other two angles will also be [tex]\(52.5^\circ\)[/tex] and [tex]\(127.5^\circ\)[/tex].
Therefore, the measures of all the angles in the parallelogram are:
[tex]\[ 52.5^\circ, 127.5^\circ, 52.5^\circ, 127.5^\circ \][/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.