Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
A triangles angles have to add up to 180 degrees. So, 180-108= 72. 72/3=24m∠A=108 m∠C= 48 m∠M=24
108+48+24=180
Answer:
m∠M=24°
Step-by-step explanation:
The sum of all the angles of the triangle is equal to 180°. It is given that Triangle ABC is similar to triangle LMN by the AA similarity postulate, therefore, similar triangles have similar set of angles. If ∠A=108°, then ∠L will also be equal to 108°, ∠B=∠M and ∠C=∠N by similarity of the triangles.
Now, let ∠M=x, then ∠B=x, also it is given that ∠C=2∠M, therefore by the sum property of the triangles,
∠A+∠B+∠C=180°
⇒108°+x+2x=180° (because ∠C=2∠M=2x)
⇒3x+108°=180°
⇒3x=180°-108°
⇒3x=72°
⇒x=24°
Therefore, m∠M=24°
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.