Answer:
The measure of angle LG, found by using
the definition of congruency and the angle
sum property is 118°
What makes two triangles congruent?
Two triangles are congruent if satisfy the following conditions
• All three sides of one triangle are congruent to the three sides of the other triangle (SSS)
Two sides and the included angle in one triangle are congruent to two sides and the included angle in the other triangle (SAS)
. Two angles and the included side of one triangle are congruent to two angles and the included side of the other trianale (ASA)
•Two angles and the non included side of one triangle are congruent to two angles and a non included side of the other triangle (SAA)
. The hypotenuse side and a leg in a right triangle are congruent to the hypotenuse and a leg in the other triangle (HL)
• An acute angle and the hypotenuse side of a right triangle are congruent to an acute angle and the hypotenuse side the other triangle (HA)
Parts of the question that appear missing includes;
ACAT = ADOG
m∠C = 25°
m2O = 37°
The measure of angle 2G is found as follows;
The order of the letters in the congruency statement indicates that angle ∠C is congruent to angle ∠D, angle ∠A is congruent to angle ZO, and angle LT is congruent to angle ZG, which from the definition of congruency, indicates that we have;
m∠C = m∠D = 25°
m∠A = m2O = 37°
m∠T = m∠G
The measure of angle LG and angle LT can therefore, be found from the angle sum property of the interior angles of a triangle.
m∠C + m∠A + m∠T= 180° (angle sum
property of a triangle)
m∠D + m∠O + mzG= 180° (angle sum
property of a triangle)
mzG = 180° - (m∠D + m2O) (subtraction
property of equality)
mzG = 180° - (25° + 37°) = 118°
The measure of angle 2G, m∠G is 118°
Learn more about the angle sum property of a triangle