In the diagram to the left ADE is an isosceles triangle. Segment EC bisects DCB. A. Find the measures of DAE, ECB, and EBC
B. Explain how you were able to find the measures of these three angles

m<DAE = 35°

m<ECB = 37°

m<EBC = 71°

Explanation:

✔️Find m<DAE

∆ADE is said to be an isosceles triangle, therefore, the base angles, <DAE and <AED are of equal measures.

Thus, m<ADE is given as 110°. Therefore,

m<DAE = ½(180 - m<ADE)

Substitute

m<DAE = ½(180 - 110)

m<DAE = ½(70)

m<DAE = 35°

✔️Find m<ECB:

We are told that segment EC bisects <DCB. This implies that <DCB is divided into two equal angles, which are <ECD and <ECB.

This means that:

m<ECD = m<ECB

Since m<ECD is given as 37°, therefore:

m<ECD = m<ECB = 37°

m<ECB = 37°

✔️Find m<EBC:

m<EBC = 180 - (m<CAB + m<ACB)

m<CAB = m<DAE = 35°

m<ACB = 2(m<ECD) = 2(37) = 74°

Plug in the values

m<EBC = 180 - (35 + 74)

m<EBC = 180 - 109

m<EBC = 71°

hello!

let's go through all of these words' definitions.

u-shaped valley - where the valley curves down like a u shape

corrie - similar to the hole created at the top of a volcano when it erupts, it's almost like a dent in a mountain

pyramidal peak - a mountain where the peak is very sharp, such as the matterhorn.

arete - two valleys separated by a thin mountain range

i'm going to assume you know how to read a topographic map, but in case you don't, feel free to comment.

now, let's figure out which one's which:

a - seems to be a mountain range separating two valleys, with a mountain running from top center to bottom center and two valleys on either side. therefore, i'd consider this an arete.

b - it looks like a dent into the mountain, like what a corrie is.

c - looks to be a valley, with two steeper sides curving up around the bottom of the valley which has a river in it. i would consider this an u-shaped valley.

hope this !