1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kumpel [21]
3 years ago
12

The perpendicular bisector of side ab of ∆abc intersects the extension of side ac at

Mathematics
1 answer:
Triss [41]3 years ago
6 0

Answer:

\angle ABC=23^{\circ}

Step-by-step explanation:

Given information: The perpendicular bisector of side AB of ∆ABC intersects the extension of side AC at D, m∠CBD = 16° and m∠ACB = 118°.

Let the measure of ∠ABC is x°.

\angle ABD=\angle ABC+\angle CBD

\angle ABD=x+16

In triangle ABD,  DM is perpendicular bisector of AB.

In triangle ADM and BDM,

AM\cong BM              (Definition of perpendicular bisector)

\angle AMD\cong \angle BMD            (Definition of perpendicular bisector)

DM\cong DM              (Reflection property)

By SAS postulate,

\triangle ADM\cong \triangle BDM

\angle MAD\cong \triangle MBD            (CPCTC)

\angle MAD=x+16

\angle BAC=x+16

According to angle sum property of a triangle, the sum of interior angles of triangle is 180°.

In triangle ABC

\angle ABC+\angle ACB+\angle BAC=180

x+118+(x+16)=180

2x+134=180

Subtract 134 from both sides.

2x=180-134

2x=46

Divide both sides by 2.

x=\frac{46}{2}

x=23}

Therefore, the measure of ∠ABC is 23°.

You might be interested in
The scatter plot shows the sizes and annual rents of some office spaces in the downtown area of a city. What would a line of bes
strojnjashka [21]
Give me a second please. Will have done in a second
8 0
3 years ago
I need help asap. anyone?
Charra [1.4K]

Answer:

D

Step-by-step explanation:

Has the correct y-axis and has the graph going the correct way for both functions.

7 0
3 years ago
Read 2 more answers
1 A baseball is struck such that its position on a plane perpendicular to home plate can be described by the equation y = (x - 1
marshall27 [118]

Answer:

21

Step-by-step explanation:

7 0
3 years ago
Write an equation in slope -intercept form for the line with slope -2/3 and y-intercept 5. Then graph
Karo-lina-s [1.5K]

Answer:

Y=-2/3x + 5

Step-by-step explanation:

5 0
3 years ago
Given that ABC is similar to DEF, solve for x.
Zina [86]
Can't without a picture :/
7 0
3 years ago
Read 2 more answers
Other questions:
  • You want to buy a new sports car 3 years from now, and you plan to save $6,200 per year, beginning one year from today. you will
    7·1 answer
  • If g(x) = 10 + 2x what is g(-3)
    7·2 answers
  • 54,860,000 round to the nearest ten million
    7·2 answers
  • a chef makes 1 and 1/2 gallon of soup in a large pot how many one cup servings can the chef get from his large pot of soup
    7·2 answers
  • Simplify xz^3*4x^4z^5
    12·1 answer
  • The graph represents a functionE(t). Describe why the graph represents a function. Identify the
    15·1 answer
  • How do you learn Vertex. Help me please
    6·1 answer
  • For which of the following conditions will the sum of<br> integers m and n always be an odd integer?
    6·1 answer
  • Hello everyone good morning may I get ur help in the first attachment~ marking brainliest for the right answer
    12·2 answers
  • Some fireworks are fired vertically into the air from the ground at an initial velocity of 80 feet per second. This motion can b
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!