### Problem Statement: Geometry - Isosceles Triangle#### Diagram:The diagram shows an isosceles triangle \( \triangle HAM \) with the following characteristics:- Vertex \( A \) is the apex of the isosceles triangle.- \( \angle A \) measures \( 32^\circ \).- The sides \( HA \) and \( MA \) are marked as equal (congruent).The vertices are labeled as follows:- \( H \) and \( M \) are the base vertices.- \( A \) is the vertex opposite the base \( HM \).#### Question:In isosceles \( \triangle HAM \), \( m \angle A = 32^\circ \). What is \( m \angle H \)?#### Choices:- \( 32^\circ \)- \( 58^\circ \)- \( 74^\circ \)- \( 148^\circ \)#### Solution Explanation:To solve for \( m \angle H \), we use the properties of isosceles triangles and the fact that the sum of internal angles of a triangle is \( 180^\circ \).Given that \( \triangle HAM \) is isosceles with \( HA = MA \), the base angles \( \angle H \) and \( \angle M \) are equal. Let \( m \angle H = m \angle M = x \).Thus, we have:\[ m \angle A + m \angle H + m \angle M = 180^\circ \]Substitute the known values:\[ 32^\circ + x + x = 180^\circ \]\[ 32^\circ + 2x = 180^\circ \]\[ 2x = 180^\circ - 32^\circ \]\[ 2x = 148^\circ \]\[ x = 74^\circ \]Therefore, \( m \angle H = 74^\circ \).#### Correct Answer:- \( 74^\circ \)---This question helps students practice understanding properties of isosceles triangles, specifically the internal angle relationships and sum of angles in a triangle.

Answered: Image /qna-images/answer/0541b1f4-f955-47e1-8a29-fe8ac0b01b28.jpg

Answered: A 320 Н M In isosceles AHAM, m&A =…

A 320 Н M In isosceles AHAM, m&A = 32°,. What is m ZH? 32° 58° O 74° 148°

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

ChapterCSR: Contents Of Student Resources

Section: Chapter Questions

Problem 1.39EP

Similar questions

(see the triangle in the picture). if ∆ABO is an equilateral triangle whose circumference is equal to 12, the value of (m + n)^(-1) is?
tion 1 2 3 4 5 6 7 8 9 ~ Construct a problem where a student needs to find the missing measure of a triangle using the midsegment equation. Provide a labeled triangle, solution and steps for solving the problem. Save
What is the area of a triangle whose vertices are (-4, - 3). (8, 7), and (8, - 3)?
The vertices of a triangle are A(-2, 0), B(0, 3), C(2, 2). Translate the triangle 4 units down. What are the coordinates of the image? Enter the coordinates in order of A( , ),B( , ),C( , ). No space in between coordinates and numbers. *
Find the area of the triangle by the points (8,-5) ,(-2,-7) and (5,1) by using herones formula
a right triangle has coordinates (-3, 4) (3, 6) and (-1, -2). what is the area of the right triangle?
Points (a, 5) and (9, b) are on the circle x^2 + y^2 = 125. Determine the possible values of a and b. Round to one decimal place. if necessarv.
Whats the area of a triangle if its vertices are at A (-8,-6), B (6,9) and C (8,-14)
Vhich point can be used to create a right triangle that nas AB as its hypotenuse? (3, -3) 2- (-8, 4) -8 2 2 (-3, 3) B. (-4, -8)
A triangle in the coordinate plane had coordinates of (2,3) (-4,5), and (-2,4). It is reflected about the y-axis. What it’s new coordinates?
Find the angle between (-1,-2) and (-6,3)
Triangle A'B'C" is created by dilating triangle 4. What is the length of A" B"?